Correlation of rural land value factors in Montana by Robert Jordan Remer A thesis submitted to the Graduate Faculty in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE in Agricultural Economics Montana State University © Copyright by Robert Jordan Remer (1967) Abstract: The market value of rural property is affected by many variable factors and conditions. The estimate of the market value of a property is used in many appraisal situations today including right of way acquisition by governmental agencies, mortgage loan appraisals, property sales and estate settlements. One of the chief problems confronted by an appraiser is the analysis or correlation of a number of market sales for trends. In this study the use of the computer in assisting a field or reviewing appraiser to analyze market information is demonstrated in three ways. First, a general tabulation of the sales in a summary manner was made. Second, a productivity rating was computed for each sale in the group and the linear regression analysis statistics of sale price (dependent variable) and productivity (independent variable) computed to better evaluate this relationship. Third, multiple linear regression statistics were computed which would evaluate particular variables in a sale data group and provide information to predict other property values from these coefficients. It is concluded that simple linear regression models may be used for the purpose of correlating a group of sales. In this model the productivity of the land is estimated and other variable factors which influence specific sales may be observed from the scatter diagram. The calculation of a composite productivity rating which considers many production factors such as soil, temperature, rainfall, elevation, etc., is the first step in this type of correlation where productivity is hypothesized to be an important influence in the price. Multiple regression statistics are more meaningful in predicting property values because many variable factors are considered, however, this model was limited by sample size in this study. Sample size proves to be a limitation frequently for field appraisers because large numbers of comparable sales are not available in specific local areas. However, this model may be used in some cases to evaluate which variables were the most important for the group of sales as a whole. The use, advantages, and limitations of multiple regression statistics to forecast property values are demonstrated in this study. Further study appears warranted to better define the relationships between the variables where they are nonlinear and to include other factors in a quantitative manner such as terms of sale. If the multiple regression model can be improved it may some day be possible to predict values for rural properties that would be within 5 percent or 10 percent of the true value for 95 percent of the cases.  CORRELATION OF RURAL LAND VALUE FACTORS IN.MONTANA by ROBERT JORDAN REMER A thesis submitted to the Graduate Faculty in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE in Agricultural Economics Approved: Head, Major Departmeri Examining Committee Gradua Bean I/ MONTANA STATE UNIVERSITY Bozeman, Montana December, 1967 iii ACKNOWLEDGMENTS The author desires to express sincere appreciation to Dr. Layton Thompson, Committee ,Chairman, under whose guidance this research study was completed. His advice and editing have improved the readability and content.of this manuscript. Sincere thanks are also expressed to Drs. Clarence Jensen, Richard McConnen, Richard Wheeler and Layton Thompson who made valuable suggestions in the development of this study and report. The author wishes to acknowledge the contribution of the officials and staff of the Montana Highway Commission and U . S. Bureau.of Public Roads. Their interest and financial assistance have made this study possible. This study would have been virtually impossible without the state wide sales data furnished by the Highway Commission District Offices, The enthusiasm, interest and cooperation of the District personnel who compiled the data was very much appreciated. Sincere thanks are.expressed to Paul R. DeVine, Robert E. Champion, and Jack Ricker who coordinated this study with the District Offices of the Montana Highway Commission, Appreciation is also expressed to James Hein of the Glendive District for the use of additional appraisal data in this report. This report has been prepared for the Montana Highway Commission in. cooperation with U . S. Department of Commerce, Bureau of Public Roads. The opinions, findings, and conclusions expressed.in this publication are those of the author and not necessarily those of the Montana State Highway Commission or Bureau of Public Roads. iv Acknowledgment is given for the guidance .and instruction extended by faculty members of the Agricultural Economics Staff at Montana State University. Likewise, thanks are extended,to the stenographic work of Mrs. Dianna Stockstad of the Agricultural Economics Department and Peggy Grisamer who typed the final copy of this report. Finally, special thanks and.appreciation are due to my wife, Janice, and family for their patience, encouragement, and assistance which has made this work possible. The author assumes sole responsibility for any possible errors or omissions in this report. VTABLE OF CONTENTS Page VITA............ ............................. . ii CORELATINFUIEDV . . . ............ . ........ . . . . . . . . . . . ill TABLE OF .CONTENTS .. . . ......... ....................... . v LIST OF TABLES....................................... vii LIST OF FIGURES ................................................. .viii ABSTRACT. .......... . . . . . . . . . . . . . . . . . . ........ x CHAPTER I. RURAL APPRAISAL TODAY . . . . . . . . ................ I CHAPTER II. TOWARD A SCIENTIFIC APPROACH TO APPRAISAL. . . . . . . 8 CHAPTER III. MATHEMATICAL DATA STUDIES AND SURVEYS . . . . . . . . 12. CHAPTER IV. EXPERIMENTAL PROCEDURE . . . . . . . . . . . . . . . . 23 Part .1. Productivity Variables— Acres/Animal Unit and ,Feed . Units/Acre. ,. . .............. ........................ 23 Part 2. . Montana Land Classifications, . . . . . . . . . . . . 25 Part 3. Crop Factors,for Production Units . . . . . . . . . . 27 Part 4. Source and Structure of Data .Groups............ 32 Part 5 o Linear Regression Model.......................... 37 Standard Error of Estimate, .................... . . . . 42 Coefficient of Determination and Correlation; . . . . . . 42 Regression Coefficient. ............ 44 Standard Error in Regression Coefficient............ . . 45 Hypothesis Testing. . . . . . . . . . . . . . . . . . . . . 46 Summary............ ................... . . . ......... 47 Part 6. Multiple.Linear Regression Model. . . . . . . . . . . 48 Standard Error of Estimate. . . . . . . . . . . . . . . . 50 Coefficients of Multiple Determination and Correlation. . 51 ■ Coefficients of Partial Correlation . . . . . . . . . . . . 51 Net Regression Coefficients . . . . . . . . . ........ . . 52 Significance of Partial Regression Coefficients . . . . . . 52 Standard Partial Regression Coefficients. . . . . . . . . 53 Part 7. Computer Processing of Data . . . . . . . . . . . . . 54 Field Coding Forms................................... .. 54 One Pass Multiple Regression Program. . . . . . . . . . . 57 CHAPTER V. DATA PROCESSING RESULTS . ............ 59. Billings Irrigated Farms. ........................ 59 Billings Wheat Farms Area . ........ . . . . . . . . . . . 59 Billings Livestock Ranches. . ............ .............. 61 Butte Irrigated Farms . . . . . . . . . . . ........ . . 61 Butte Wheat Farms . ....................................62 Butte Livestock Ranches ................................. 62 TABLE OF CONTENTS. (continued) Page Glendive Irrigated Farms . . . . . . . . . . . . . . . . . . . . . 62 Glendive Wheat Farms. . .................... 63 Glendive Livestock Ranches. . . . . ........ . . . . . . 63 Great Falls Irrigated Farms . .......................... . 64 Great Falls Wheat Farms . . . . . . . . . . . . . . . . . 64 Great,Falls Livestock Ranches . . . . . . . . . . . . . . 65 Missoula Irrigated Farms. .............. 65 Missoula Livestock Ranches. . . . . . . . . . . . . . . . 65 Summary,of.District Areas . . . . . ........ . . . . . . 66 Tabulation Reports. . ...................... 69 Linear Regression Statistics. . . . . . . . . . . . . . . 69 Time Adjustments of Sales Prices. . . . . . . . . . . . . 70 Multiple Regression Statistics. . . . . . . . . . . . . . 75 Predicting Sales Price with Multiple Regression Coefficients. . . . . . . . . . . . . . . . . . . . . . 81 Project -Report Analysis . . . . . . . . . . . . . . . . . . 82 CHAPTER VI. EVALUATION OF RESULTS., . . . . . . . . . . . . . . . . 90 Productivity Variables, Feed Units per Acre and Acres per Animal Unit. . . . . . . . . . . . . . . . . . . . 90 Linear Regression Model . . . . . . ........ . . . . . . 91 Multiple Regression Model . » . ,........... 96 Time. . a * o . . . o . . . e * . o * * . . . . . o e . o » 97 Summary . . . . . . . . . . . . . . . . . .......... . . . 98 CHAPTER.VII1 SUGGESTIONS FOR FURTHER STUDY . . . . . . .......... 100 APPENDICES. . .............................'.......... . 102 APPENDIX A= Statistical Formula Study for the Linear Regression Model. . . . . . . . . . . . . . . . . . . . . 103 APPENDIX.B . Tabulation Reports Showing Sales Adjusted and Unadjusted for Time . . . . . . . . . . . . . . . . . . . 106 APPENDIX C. Sample.of Linear Regression Graph . . ........ . 138 APPENDIX D . One Pass Multiple Regression Output . . . ..... . 142 APPENDIX E = Predicted Values of Sales . . ....... 164 LITERATURE■CITED . . 178 LIST OF TABLES Number. Page - I CONSIDERATIONS INFLUENCING THE PRICE BUYERS PAID FOR LAND IN MONTANA, 1956, 1957..................................... 19 II MONTANA LAND PRODUCTIVITY CLASSIFICATIONS USED FOR TAX ASSESSMENT PURPOSES . . . . . . . . . . ................... 26 III NUTRIENT REQUIREMENTS AND ANIMAL UNITS PER MONTH FOR LIVESTOCK FROM APPRAISAL TERMINOLOGY HANDBOOK 28 IV METHOD OF ARRIVING AT.THE POUNDS OF TDN REQUIRED FOR ONE ANIMAL UNIT ■ MONTH ,.............. ........... .. . , 29 V FACTORS USED TO■CONVERT PHYSICAL PRODUCTION OF CROPS INTO AUM' S OF FEED.. . ........................................... 30 VI VARIABLES,CONSIDERED IN MULTIPLE•REGRESSION-ANALYSIS OF FARM AND RANCH - SALES. . ... .-. ... ... . . . . . ■. . . 36 VII COMPARISONS OF SALE GROUPS IN DISTRICT AREAS— PART I. . . . 67 VIII COMPARISONS OF SALE GROUPS IN DISTRICT AREAS— PART II . . . 68 IX INDEX FIGURES FOR SALE PRICES OF MONTANA LAND (1957-1959 = 100) .............................................. 74 X ADJUSTED ANNUAL PERCENT CHANGE IN PRICE OF IRRIGATED LAND IN MONTANA.................................. 74 . XI AVERAGE OF r2 VALUES FOR SALES GROUPS BY CONSIDERING SEPARATE DISTRICT r2' VALUES i' -. . •. ... . . ... . . ... . . 75 XII S1UMMARY OF RESULTS OF THE LINEAR REGRESSION MODEL BY DISTRICT :WITH ,SALES UNADJUSTED FOR TIME . ... . . ... . . .76 XIII SUMMARY OF RESULTS OF - THE LINEAR REGRESSION MODEL BY DISTRICT WITH SALES ADJUSTED FOR TIME 77 XIV AVERAGE R2 VALUES FOR SALE.GROUPS BY CONSIDERING SEPARATE• DISTRICT R2'VALUES. . . . . . . . . . . . . . . . . . . . . . 78 XV• RELATIVE FREQUENCY OF SIGNIFICANT VARIABLES FROM MULTIPLE ' REGRESSION ANALYSIS FOR ALL GROUPS OF SALES . . . . . . . . 79 vii viii LIST OF'TABLES (continued) Numb er Page XVI RELATIVE FREQUENCY•OF SIGNIFICANT VARIABLES FROM MULTIPLE REGRESSION FOR COMBINED GROUPS OF SALES. . . . . . . . . . . . 80 XVII SUMMARY OF RESIDUALS BY ■ TYPE OF SALES.......................82 . XVIII' MULTIPLE LINEAR REGRESSION EQUATION COEFFICIENTS FOR IRRIGATED FARMS. . ... . . '. . . . . ,. . ■. ... . . ... . . . 83 XIX MULTIPLE LINEAR REGRESSION EQUATION COEFFICIENTS FOR WHEAT FARMS . . . . ■ .............. . . . . ■. . ,. . •. ... . .... .84 XX MULTIPLE LINEAR .REGRESSION EQUATION COEFFICIENTS FOR LIVE­ STOCK RANCHES. . . . . . . . . . . . . . . . . . . . . . . . . . 85 XXI SUMMARY OF MULTIPLE LINEAR REGRESSION MODEL BY DISTRICT, . . 86 XXII PARCEL PREDICTIONS BASED ON FARM SALES INFORMATION OF PROJECT I IG 94-3(9)76 IN THE GLENDIVE DISTRICT. . . . . . . 89 XXIII HEADINGS. USED IN THE TABULATION REPORT - . . . . - . . . . ■. . ..107 Number Page ix LIST OF FIGURES 1 1959 Sale-Prices of■Non-Irrigated, Tillable Land in Three Montana-counties............ -.o . . . . . . . . 17 2 1959 Sale Prices of Tillable Irrigated Land in Montana. . . . 20 3 1959 Sale Prices of Non-Irrigated Farm Land in Montana. . . . 20 4 1959 Sale Prices .of Range Land in Montana..................21 5 Scales to Convert Feed Unit,per Acre Ratings into Crop Production Ratings...................................... .. 33 6 Scatter Diagram Illustrating Correlation of Sales Graphically 40 7 Illustration of Standard Error of Estimate;in Simple.Regres­ sion Analysis ........... 43 8 Coding Form.to Record,Raw Sale Data— Page A .......... . . . 55 9 Coding Form, to Record ,Raw "Sale Data— Page B . . . . . . . . . . 56 10 District Areas of.the Montana Highway. Commission and Source. Areas of Sale Data. . .....................60 11 Graph of,Linear Regression Trend Lines for the Groups of Irrigated Farms Sales by Districts and All Districts Combined........■......... ........................... .. 71 12 Graph of Linear Regression Trend Lines for the Groups of Wheat Farms Sales by Districts and all Districts Combined . . 72 13 Graph of,Linear Regression Trend Lines for the Groups of. Livestock Ranch Sales by Districts and All Districts Combined* . . . . . . . . . . . . . . ............ . . . . . . 73 14 Graph of Sales and Appraisals on Project I IG 94-3(9)76 . . . 88 15 Hypothetical Subject Appraisal Shown in,Relation to the Most Comparable Market Sales . ........ . . . . . . . . . . . . . 92 16 Comparison of Hypothetical Market, Appraisal and Loan.Trends. 93 X - LIST OF FIGURES (continued) Numb er Page 17 Investment per Feed.Unit of Irrigated Farms at Two Levels of Productivity . . . . ............................. ........... 94 18 Investment.per Animal Unit of Livestock.Ranches at Two Levels of Productivity..................................' o .........94 19 Investment per Feed Unit of Wheat Farms at Two Levels of Productivity . . . . . . . . . . . . . . . . . ........ . . . 95 20 Mid Range Approximation of Non-Linear Sales Distribution . . . 96 xi ABSTRACT The market value of rural property is affected by many variable factors and conditions. The estimate of the market value of a property is used in many appraisal situations today including right of way acqui­ sition by governmental agencies, mortgage loan appraisals, property sales and estate settlements. One of the chief problems confronted by an appraiser is the analysis or correlation of a number of market sales for trends. ■ In this study the use of the computer in assisting a field or reviewing appraiser to analyze market information is demonstrated in three ways. First, a general tabulation of the sales in a summary manner was made. Second, a productivity rating was-computed for each sale in the group and the linear regression analysis statistics of sale price (dependent variable) and productivity (independent variable) computed to better evaluate this relationship. Third, multiple linear regression statistics were computed which would evaluate particular variables in a sale data group and provide information to predict other property values from these coefficients. It is concluded that simple linear regression models may be used for the purpose of correlating a group of sales. In this model the produc­ tivity of.the land is estimated and other variable factors which influence specific sales may be observed from the scatter diagram. The calculation of a.composite productivity rating which considers many production factors such as soil, temperature, rainfall, elevation, etc., is the first step in this type of correlation where productivity is hypothesized to be an important influence in the price. Multiple regression statistics are more meaningful in predicting property values because many variable factors are considered, however, this model was limited by sample size in this study. Sample size proves to be a limitation frequently for field appraisers because large numbers of comparable sales are not available in specific local areas. However, this model may be used' in some cases to evaluate which variables were the most.important for the group of sales as a whole. The use, advantages, and limitations of multiple regression statistics to forecast property values are demonstrated in this study. Further study appears warranted to better define the relationships between the variables where they are nonlinear and to include other factors in a quantitative manner such as terms of sale. If the multiple regression model can be improved it may some day be possible to predict values for rural properties that would be within 5 percent or 10 percent of the true value for 95 percent of the cases. CHAPTER I RURAL APPRAISAL TODAY The idea that the value of real estate is based on the benefits that may be received from its ownership or use is a fundamental concept. The benefits which may be received from the ownership or use of real estate include income, homesite, occupation, recreation or prestige. These benefits of real estate will vary with time, location, and the very nature of a particular tract. Legal claims to the benefits of real estate may be termed property or-property rights. I/ The appraisal of a tract of real estate then becomes a matter of estimating the value of the benefits which are anticipated to accrue in the future. Rural property usually is thought to be property outside of a city or.urban area. An agricultural property is one which is located in a rural area with a highest and best use of agricultural production. The usual boundary separating urban and agricultural property is a transi­ tional zone. A transitional property may have a non-agricultural highest and best use as a whole, yet that part of the property which is tillable or grazing land may remain in agricultural production. Rural homesites, recreational areas, and commercial sites with excess land along highways may be examples of this type of transitional real estate. A transitional property may have a highest and best use as an agricultural producing unit I/ The word property is most often used to mean that which one owns such as goods.or tract of land.• Property may also be the right of posses­ sion, enjoyment, or disposal of something tangible. but have a higher price due to the potential for future urban development. A careful study of the sales and market trends in an area should indicate whether the highest and best uses of a rural property is for agricultural production only or as a transitional property. An appraisal of rural property may be made for such purposes as fair market value, insurance value, loan value or tax value. The number of appraisals for market value has greatly increased in recent years. The increase in numbers of market value appraisals has been largely due.to the appraisals made for governmental takings. Right-of-way acquisition for interstate and other highway takings require market value appraisals. Likewise,'right-of-way is necessary for dams, flood control, power lines and other public projects. In many cases a market value appraisal is made separately for the land owner at his request in addition to the one made by the governmental agency. In most instances, appraisals made for loan purposes.are market value appraisals or some proportion of market value. Market value may relate'directly or.indirectly in.an insurance, appraisal on improvements. For the various purposes for which an appraisal is made, market value overall is the most important considera­ tion. During the past 40 to 50 years, rural appraisers have considered and used the three basic.approaches to value in varying degrees. These approaches to value are the income approach, cost approach and market data approach. The income approach utilizes a net income estimate for the property which is capitalized into an indication of value. The cost approach sums the value of the vacant land and.the depreciated value of - 2 - the improvements. The market data approach is one of overall comparisons between the subject property which is being appraised and the comparable sales. Appraisal situations may warrant the use of one or.all three approaches to value. In particular cases one or two of the approaches may be limited in use or inappropriate. In many agricultural situations the cost approach is not found to be.appropriate for the reason that the reproduction cost of the buildings less depreciation may not reflect the true contribution value of the buildings to the property as a whole. The income approach frequently is limited or difficult to apply because of the problems involved in interpreting a proper capitalization rate. These limitations to the cost and income approaches leave the market data approach most widely used either as the sole approach or in conjunction with the two other approaches. If more than one approach to value is used, a correlation is made to arrive at a final estimate of value for the property. The information which is necessary for the use of any one of the.three approaches to value must come primarily from the market. The appraiser's job is to study the market. A study of the market means a study of comparable sales in the area and other pertinent economic.data including population, income, and development trends. The analysis of comparable sales is the key to discovering how people have acted with respect to particular types of property in.the past. A good understanding of.comparable sales may well become a basis for predicting or estimating how the subject property would be considered if put up for sale. It is a - 3 - — 4 — basic truth that fair market values are determined only in the market and this market must be studied carefully by the appraiser. One of the first problems that arises in the use of the market data approach in making overall comparisons of sales with the subject property is the finding and selecting of the most comparable sales. Sale properties will not be exactly like the subject and may differ in many respects. A subject property which has been sold in recent years may also have been changed by improvements or deterioration. Even if the subject was sold recently a careful analysis is necessary to determine if the sale was a fair market transaction.■ Sale properties may be studied for apparent trends and special differences that may reflect information for the particular subject. Although properties and conditions of sales vary, the market is often found to have some degree of uniformity. A study of.the market involves many transactions but such factors in our economy as the prin­ ciples of substitution and competition force a uniformity in the actions taken. For this reason it is important to study variables common to all the sales. Correlation becomes important in interpretating the differences between the sales. A point should be made about correlation in the appraisal process. Correlation begins in the studying of the appraisal problem, market conditions, and comparable sales and continues throughout the appraisal study and report. TJ A very useful and important technique in correlating comparable sales is the discovery and use of meaningful units of measurement common to all of the sales. A study of sales in a particular agricultural area may reveal that buyers and sellers think in terms of dollars per.acre. In some other area the common unit may be dollars per animal unit. As the size of the farm or acreage decreases, buyers and sellers may react to the site as a whole including land and buildings together. What are the principle factors responsible for the price fluctuations or differences within the group? Any appraiser, of course, is quick to recognize that there are many factors which may be causing variations in price right• down to the very impulses of the buyer and seller at the time of the sale. Measurable factors such as land quality, buildings, location, financing and size may be contributing to price differences between the sales. In many cases it is a difficult if not impossible,task.to determine how much particular attributes contributed to a particular sale price with all • other things being equal.. An analysis of how much particular attributes contributed to the sale prices involves multiple correlation analysis. - 5 - T J . American Institute of Real Estate Appraisers. The Appraisal of Real. Estate, American Institute of Real Estate Appraisers, 36 South Wabash Avenue, Chicago 3, 111., 1961, p. 196. 6The most important factors affecting rural sales will vary as to type and■importance for any specific area or time. The importance assigned to various factors by different appraisers who are interpreting the.same market often varies. This situation can easily lead to disparity between individual appraisers. Some modern computing techniques may assist an appraiser who is making a market study. The actual techniques or mathematical processes may not,be new, but computers have speeded up the processes. One example of computer use is in the computation of a mathematical estimating equation which is based on several independent variable factors. Another example of computer use is in the cataloging of comparable sales for ready access and recall for a particular area. The computer may also be used to great advantage in preparing tabulation summary reports. The problem facing real estate appraisers boils down to one.of putting more logic and evidence into the appraisal. 3/ It is important to be able to ,support an estimate of value for a client by more than statements of general opinion or vast experience. More considerations must be taken into account in modern appraisals due to the growing complexities of our society. The problem of putting more logic and evidence into an appraisal is not an easy one. One thing an appraiser often would like to know is how much weight to give particular attributes of a property. To attempt 3/ William G. Murray, M.A.I., "Challenge Facing Real Estate Appraisers Today", The Journal of American Society of Farm. Managers and .Rural ■ Appraisers, April 1961, p. 55. 7to assign contribution amounts for various factors requires a careful measurement of many details• The problem of putting more evidence into an appraisal may be dealt with by a better selection of the comparable sales which are used in making over all comparisons and correlations. A better selection of comparable sales may reduce the disparity between appraisers where two or more independent appraisals are made for one property. A better selection of comparable sales may be possible if the sale properties are carefully correlated amongst themselves by some common unit of measurement = The problems of rural appraisal are many and varied. Some of these problems are the same ones that were present in the early days of the profession of farm appraisal. However, some progress has been made to put rural appraisal on a more scientific basis-. The use of three approaches to value, where appropriate, offers a basic plan to get the appraiser started on the way to an estimate of value. In more recent years emphasis has been placed on the analysis of data. Mathematical techniques to analyze market data and predict a value for a,subject property have received more attention in recent years due to a desire for finding better ways of estimating a value for a property and because of the availability of high-speed computers. The future of professional. rural appraisal depends on the ability of appraisers to be able to make accurate analysis of the market. CHAPTER TI TOWARD A SCIENTIFIC APPROACH TO APPRAISAL The many problems which confront■appraisers today indicate a need for better data analysis and methods of appraisal. A few specific problems which confront appraisers were noted in the previous chapter. A problem that often exists is that one or two of the three approaches to value may not be appropriate for use. Clients today are asking for more examples of data from the market to support estimates of value. In many instances a great disparity may exist between two appraisers on a particular appraisal. In the past 10 years there has been a growing need for the best, most accurate appraisals in right-of-way work of various govern­ mental agencies. Better processing equipment in the form of computers offers a great advantage in tackling these problems by making detailed, scientific data studies more feasible. However, high speed processing alone won't solve these problems. There is a need for better, more complete, scientific data analysis techniques for rural appraisal. Most of the work in recent years which has been characterized as "scientific appraisal" has involved an increased use of mathematics with emphasis on price prediction through multiple regression analysis. However, very few multiple regression equations have shown spectacular predicting qualities. Modern computers have made it possible to make studies with a large number of variables with the hope that a better system of price prediction can be developed. However, market variation is always a problem for an appraiser. A good multiple regression esti­ mating equation depends wholly upon,the market area and.the ability of the appraiser to discover the variables to be included. It is hoped that by further study of market situations and variables, better estimating equations may be developed. Recognizing the problems and limitations of good multiple regression estimating equations, a different approach to the problem of making rural appraisals more scientific seems to be warranted. This approach is to find one variable which takes into account a.number of factors and explains a major amount of the market variation in sales price. An overall produc­ tivity rating which considers land type, topography, climate, temperature, rainfall, growing season,etc., would be a logical variable to consider for rural properties. A graphical picture of the correlation between sales price and the productivity variable may be easily made for a number of sales. A plotting of the group of sales on a graph may allow observing the effect of other variables. Frequently some "special variable" doesn't affect more than a few of the sales in the group. The graph or scatter diagram may provide the beginning analysis of farm or ranch sale data. This analysis is the correlation of the sales amongst themselves. A graph with its correlation relationship may enable an appraiser to better select the most comparable sales from the entire group. In addition, such a graph might provide a better overall picture of the market to a client. Statistics may be used to evaluate some of the characteristics of the scatter diagram and trends. The discovery of a variable or overall unit for rating farm produc­ tivity offers some other very important uses. An important advantage of - 9 - 10 - using an overall productivity rating is that the various parts of a. property may be evaluated based on their contribution to the whole, Two examples of where contribution value of parts of a farm are important in farm mortgage loan appraisal and highway right-of-way appraisal. Frequently, in farm mortgage loan appraisal it is desired to know what value per acre should be alloted to a particular tract which is being released from the mortgage. In highway right-of-way appraisal it is often necessary to allocate a value to various classes of land which are taken or depreciated but where specific sales of particular types of land are not available or appropriate. In either farm mortgage loan appraisal or highway right-of-way appraisal it may be observed that a particular tract of land contributes more to the unit on a per acre basis•than independent sales of that type land. The reverse situation may be. observed in other instances. The placing of emphasis on a.simple linear model should not be thought of as making a multiple regression study useless. Multiple regression is more realistic in any predicting sense because it recog­ nizes many factors. However, some of the advantages are often limited by sample.size and market characteristics. In spite of these limitations it is still highly desirable to study a market with this technique. The predicting qualities of an estimating equation may be evaluated, In addition, some idea of the significance and rank of independent.variables may be obtained. 11 - Both the linear and multiple linear regression model.are hypothe­ sized to add meaningful information to an appraiser. The hypothesis to be tested then is that a .statistically significant overall productivity variable may bexfound and used in the linear regression model. For the multiple regression model, it is hypothesized that a statistically significant model may be.developed which explains market variation and. that,significant variables may be delineated. CHAPTER III MATHEMATICAL DATA STUDIES AND SURVEYS Some early attempts to use mathematical techniques such as multiple regression analysis to study real estate market variables and estimate values date.back.to the 1920's. However, appraisal literature frequently has warned against the use of mathematical formulas for the purpose of. estimating values. Instead, experience has long been heralded to be the mark of an expert along with professional society affiliation. Many people have tried to bring a greater degree of science to the art of appraisal through such techniques as multiple regression analysis, but until the development of modern computers in recent years, multiple regression analysis meant many hard tedious hours of.calculations. Large models would be.highly laborious to do by hand calculations. A summary of some of the attempts at scientific appraisal through multiple regression analysis has been made by Edward F. Renshaw, kj In his discussion of the case for an econometric approachj he.notes that although it may be hopeless to isolate all the factors which buyers take into consideration when purchasing a property, it is possible to estab­ lish a correlation between real estate values and.a select sub-set of determining variables. 5/ It is not necessary to have the perfect model, only one which can predict real estate values with sufficient accuracy. 4/ Edward F . Renshaw, "Scientific Appraisal", National Tax-Journal.. Vol. XI, No. 4, December 1958. 5/, Ibid., p. 319. 13 - It is possible to make a comparison of.the variances in the appraisals made by this and other methods. Several multiple.regression studies that have been done in the past years are cited in the paragraphs that follow. The purpose for citing these examples of■statistical analysis is to illustrate the . types of problems encountered and some of the variables considered. In 1922, G. C. Hassi conducted' a study in Minnesota for farms sold during the period 1916 - 1919. 6/ The factors included in this multiple regression study were depreciated cost of buildings per acre, land classi­ fication index, soil index, and distance to market. These four.factors explained 65 percent of the sales price variation. Another study during the same period of time was conducted by H. A, Wallace in 1925. TJ Here four factors were correlated with census esti­ mates of bare land values in 99 Iowa counties. The factors used were 10-year average corn yield per acre, percentage of land.in corn and in small grain, and percentage of land not plowabIe, With these factors, 84 percent of the sales price variation was explained. Wallace points out that county differences exist due to such things as metropolitan influence where the multiple regression formula doesn't make any special allowances. (J G. C. Hassi "Sale Prices as a Basis for Farm Land Appraisal", Minn. Agr. Exp. Sta. Tech. Bui. 9, 1922. This Bulletin is noted in William G. Murray's Farm Appraisal, Iowa State College Press, 3rd Ed., 1954, pp. 288-290. Tj ■ Henry A..Wallace, "Comparative Farm-Land Values in Iowa", Journal of Land and Public Utility Economics, II, No. 4, October 1926, pp. 385-392. 14 - Adjustments would also need to be made to include buildings. He further points out that such formulas will obviously apply only where the type of farming is fairly uniform. One limitation encountered in the Wallace Study was that value estimates were based on census figures which were largely estimates on the part of.farm owners of their farm values. In a study conducted by Mordecai Ezekiel, 1936, the multiple correla­ tion of eight factors linearly accounted for 41 percent of the price varia­ tion. _8/ ■ However, curvilinear correlation yielded,a higher percentage of explained variation, 60 percent. Buildings accounted for 44 percent of the variation in farm value and were separated into.three factors: dwellings, dairy buildings, and other buildings. Other factors included were crop index, percentage area tillable, percentage level land, type.of road; and distance to town. A strong case is made.for the use Of statistical methods for farm appraisal by Irving F . Davis, Jr. 9/ ■ This ,case develops out of a need for reducing disparity between individual appraisers who appraise the 8/ William G..Murray notes a study by Mordecai Ezekiel entitled "Factors Affecting Farmers’ ,Earnings.in Southeastern Pennsylvania"', U.S.D*A. Bulletin 1400, 1936, in his book Farm Appraisal, Iowa State College Press, 3rd Ed., 1954, pp.,288-290. 9/ Irving F . Davis, Jr., A Statistical Approach to Real Estate Value with Applications to. Farm Appraisal, California Division of Real Estate, Sacramento, California, 1965. ' 15 - same property. This study considered some 50 independent variable factors. Specific factors related to cotton farms, vineyards, ranches, citrus, dry grain farms and irrigated farms. Variables which were used included ones usually thought of such as size, date of sale, distance to town and some more obscure but.potentially significant ones such as soil profile, growing season and distance to nearest road. Much could be said for the careful inclusion of many variables where the computer selects those which are most significant. However, one question that exists with any study of this nature is whether this many detailed variables are evaluated individually in the minds of buyers and sellers at the time of sale. This study well points out the advantages that could come if it were possible to predict sale prices that would be within 10 percent of true value in 95 percent of the cases» Multiple regression analysis hasn’t been restricted to rural prop­ erty. Several multiple regression studies have been conducted dealing with city homesites. One study in recent years which involved residential sales in Washington, D. C., was made by William C. Pendleton. 10/ Here the selling price was estimated from such factors as log of size of house, driving time to central business district, log of size of lot, if brick, if basement, log of number of baths, if extras, median income level of 10/ William C. Pendleton, "Statistical Inference in Appraisal and Assessment Procedures", Appraisal Journal, January 1965, pp. 73-82 . 16 - area, age of house, stories, and detachment. A particular feature to be noted in this study is the weighting of particular factors by the use of logarithms. For example, it is hypothesized from costs, etc. that 100 additional square feet of house added.to a house.in the 900 square foot category makes more of a value difference than a 100 square feet difference in the 1,800 square feet category. The variables chosen in one model explained 86 percent of the variation and each variable except one was significant,at the 95 percent level. Such a test for significance indi­ cates that there is less than one chance in twenty that the universe from which these samples were drawn does not display a positive association between selling price and each of the.independent variables. A pilot study of residential property values has been undertaken by 0. R. Golan. 11/ After a choice of.independent variables was made and the multiple regression equation determined, a prediction of each sale was made by putting the sale into the equation and computing a predicted value. The results indicate that the estimates based on the multiple regression were within 5 percent, 68 percent of the time and within 10 percent, 95 percent of the time. Not all regression studies have been multiple regression although this method recognizes the influence, of many factors affecting price.. A study was conducted by Gerald Drew where linear correlations were made 11/ 0. R. Golan, Organization and Control of.Right-of-Way Functions Through the Implementation of the Multiple.Linear Regression Equa­ tion in Estimating Fair Market Value of Real Estate, The State Road Commission of West Virginia, 1966. 17 - between sale price per acre and productivity of farms in the wheat area of Montana. 12/ In this study sales from three counties were considered as separate groups. The amounts of explained variation were as follows: Chouteau County, 20 percent; Fergus County, 56 percent; and Judith Basin County, 7 percent. When the sales were combined, 23 percent of the varia­ tion was explained. The results for Chouteau and Judith Basin counties in particular show that factors other than productivity were important in determining the sale price per acre. The following graph shows the trend lines obtained for the three groups. Figure I. 1959 Sale Prices of Non-Irrigated, Tillable Land in Three Montana Counties. 12/ Gerald Drew, Derivation of a Basic Schedule of Values by Grade for the Non-Irrigated Tillable Farm Land Classification in Montana, Master's Thesis, Montana State University, Bozeman, Montana, December 1960, pp. 28-45. - 18 - A survey was conducted by Jotin D. Lawrence, Jr. , in 1957 where a group of farm purchasers was questioned about considerations that influ­ enced their purchase. 13/ The nuihber of farmers who bought.land between January I, 1956 and March 31, 1957 in the areas of Billings, Lewistown and.Glendive, Montana, totaled 102. The reasons for purchase were: Table I (page 19) has been taken from this thesis showing the percentage of,purchasers responding affirmatively to questions of consideration. A detailed study was made by Dr. Layton Thompson, of Montana land prices by grade of land in 1959. 14/ This study included over 1,400 sales on a state-wide basis. These sales were grouped into three categories, namely irrigated farms, dry farms, and livestock ranches. All prices were based on a 1959 price level. The following graphs serve,to show relative price levels. An equation for livestock ranches was not derived, but the acres per A.U . of the study has been converted from a 10-month basis to a year-long basis with the data shown in Figure 4. (page 21) 13/ John D. Lawrence, Jr., The Effect of Increasing Farm Size on Land Values, Master's Thesis, Montana State University, May 1958, pp. 1- 27. 14/ Layton S'. Thompson, "Sale Prices of Montana Agricultural Land by Class and Grade", Mont. Agr. Exp. Sta. Bul. 583, Montana.State University, Bozeman, Montana, December 1963. Reason Given Percent, Rural Residence Bought for Enlargement Bought for Strategic Value A Tenant Moving to Ownership Investment Purpose 11 58 15 8 8 19 TABLE I. CONSIDERATIONS INFLUENCING THE PRICE BUYERS PAID FOR LAND IN MONTANA, 1956, 1957. 15/ ' ____________________Price Determining Factor____________________Percent 1. Buyer placed judgment on commercial appraisal 1 4 2. Buyer sought outside help on appraising 21 3. Buyer knew of.recent sales and based judgment on such sales 20 4. Buyer estimated what land was worth based on the Way he expected to use it 77 5. ■ Terms of purchase influenced consumation of sale 40 6. Other things that influenced price and sale such as mineral rights, grazing permits, wheat acreage allotments 18 7. Buyer bargained on price 45 a. Buyer bid lower than asking price and paid.less. 39 b. Buyer bid lower than asking price but paid asking price . 6 15/ Lawrence, op. cit., pp. 1-27. 20 - 16.79 + 70.89 X 0.20 Tons of Alfalfa per Acre Figure 2. 1959 Sale Prices of Tillable Irrigated Land in Montana. 16/ .3246 Bushels of Wheat per Acre Figure 3. 1959 Sale Prices of Non-Irrigated Farm Land in Montana. 17/ 16/ Thompson, op. cit., p. 13. 17/ Ibid., pp . 10-15. 21 - < 75 S 25 O 10 20 30 40 50 60 70 80 90 Acres/Animal Unit - Year Long Figure 4. 1959 Sale Prices of Range Land in Montana. 18/ The use of mathematical models and the econometric approach appears to be well on the horizon of the appraisal profession. Particular prob­ lems that exist are mainly along the lines of data collection and variable selection. To have a data program involves intense studies in the market areas and the recording of information on relevant variables for each sale. Variable selection is a study on its own. Not only must many possible variables be considered but also their relationship to sale price must be studied. Many relationships are not linear. Further, some variables of a sale may be limited to that sale only. The advantage of models is that they may be utilized in many areas as a model. Data may be used in more than one area where there is statistical similarity. Or the model may be used with a change in variables. 18/ Ibid.. pp. 10-15. 22 - This discussion so far has been centered on statistical regression analysis of farm and ranch sales. Regression analysis is not the only mathematical tool that offers promise to appraisers . The methods of linear programming may also be used. Appraisal problems often demand the consid­ eration of the best combination of facilities in an area to determine the highest and best use. If a commercial site is to be developed with motels, supermarkets, offices, etc., there are many limiting factors that must be considered. In other words, the possibility of these various enterprises is subject to many conditions and limitations. Linear programming is mentioned here because it is one of the econometric tools available to an appraiser and falls under the heading of mathematical models. Modern computers play a key role in any of these analyses for the reason of being able to process data quickly. The computer must be recognized as an invaluable aid in,the progress of scientific appraisal and data analysis. The fact must not be overlooked that much of the progress up to this time in the ,way of mathematical models has been done by.patient researchers who worked diligently with hand calculating methods. CHAPTER IV EXPERIMENTAL PROCEDURE Part I. Productivity Variables— Acres/Animal Unit and Feed Units/Acre The animal unit concept is one commonly referred to in ranch areas of the country. Comparisons of range land are often made on the basis of acres per animal unit as a measure of its carrying capacity-. This acres per animal unit figure is an estimate for a certain range area and related to a specific grazing period. ' A more fundamental unit of compar­ ison is acres per animal unit month (AUM). A particular ranch or pasture unit ,may then be measured or rated in terms of its total carrying capacity This allows for a stocking rate variation such as double stocking for half,the normal grazing period. An example may serve to illustrate,the AUM idea more clearly. A certain range area of eastern Montana may be.rated at 45 acres per animal unit (A/AU) for a 10-month grazing season. This converts to 4.5 acres per animal unit month. . If the range area in this example contained.450 acres.there would be. 100 AUM's of feed available. This range area could theoretically be stocked at 10 AU for the full 10-month period or 20 AU for a 5-month period. The definition of one.animal unit varies slightly in different areas of the country. The animal unit concept which is used in this study is as defined by the American Society of.Range Management. 19/ 19/ Donald L . Huss, Chairman, Range Term Glossary Committee, A Glossary of Terms Used in Range Management, The American Society of Range Management, Portland, Oregon, 1964, pp. 7-8. 24 - The animal.unit is defined as one mature cow with calf or equiva­ lent. The Animal Unit Conversion factors generally accepted are: mature bull, 1.25; weaned calf, 0.6; yearling over 12 months and under 17 months, 0.7; yearling from 17 to 22 months, 0.75; two-year old from 22 months to 32 months, 0.9; mature ewe with lamb, 0.2; and grown horse, 1.25. Some appraisers talk about a feed unit which is the amount of feed required for one animal unit. The feed unit idea is used in this study for farms. The.total production of crops.and range may be converted into AUM's or AU's of feed. ■ The overall acres per animal unit variable may be used as a single factor to rank productive qualities between ranches. All crop and range production is estimated in terms of AUM's to accomplish this. Similarly, feed units per acre serve to compare farms. The conversion of crops and hay into AUM's of feed may be made by considering the total digestible nutrients (TDN) of particular feeds used in rating each type of crop land. A factor for each feed may be used in making this conversion. To derive the farm or ranch overall rating of feed units per acre or acres per animal unit respectively, employs.the land classifications as described in the sections of.this report on Montana County Assessment and special crop factors. An overall rating of a farm or ranch serves■ the appraiser in a particular way. The appraiser is able to think of the farm as a whole and not as a sum of many parts. 20/ The success of such a 20/ William G. Murray, Farm Appraisal and Valuation, Iowa State University Press, Ames, Iowa, 4th Ed., 19bl, p. 191. 25 system of overall ratings depends to a great extent on how accurately classes of .land, crop production, etc., may be defined and evaluated. Where production units are employed to provide an overall farm rating, the first step must be to have all the production of a farm converted to some common unit of production. 21/ Other systems may be used to convert, individual components of farm production to a common unit besides using TDN-factors. As an example, another conversion system might employ net energy figures instead of TDN figures. Part 2. Montana Land Classifications A system of,land reclassification for Montana in terms of crop production was developed out of the 1957 Montana Law. The work of reclassifying lands by the counties was nearly completed by 1963. These records for each farm are kept up to,date -by county land.appraisers and classification personnel. For the purpose of tax assessment all agri­ cultural lands are thus classified by type and estimated productive quality. A general schedule of land grades and production ratings was adopted by the State Board of Equalization. This schedule and the classifications, of lands on each farm have been used in this study to develop and overall productivity rating for each.farm. The general state-wide land classifi­ cation schedule which wa,s used is summarized, in Table II below. '22/ 21/ Ibid.','pi 192. ' 22/ The schedule of Montana Land Classification is taken from Procedure and Instructions for Land Reclassification by the Montana State Board of Equalization. 26 - TABLE TI. MONTANA LAND PRODUCTIVITY CLASSIFICATIONS USED FOR TAX ASSESSMENT PURPOSES. Irrigated Land T/A (Alfalfa) Grazing Land A/AUM IlA 4.5 and over GlA 1.0 and less IlB 4.2 GlB 1.4 12 3.7 G2A 2.0 13 3.2 G2B 2.3 14 2.7 G3 3.3 15 2.2 G4 4.6 16 1.7 G5 7.7 17 1.2 Dry Crop Land Eu. Wheat/A F1A2 32.0 and over FlAl 29.5 FlA 25.5 FlB 22.5 F2A 20.5 F2B 18.5 F2B 16.5 F2C 14.5 F3B 12.5 F4A 10.5 F4B 8.5 F5 Under 8.0 All irrigated lands are classed as "I" and rated in tons of alfalfa hay. Grazing land is rated in acres per animal unit month and classed as "G". This A/AUM figure is arrived at by dividing the A/AU figure for each class by the grazing period. All dry crop land is rated in bushels of wheat per acre and noted as "F". Dry crop land is considered to be onerhalf summer fallow where summer fallow is typical. The means of the general schedule were used for this modified schedule. The subclass 27 - numbers for eacfc grade.of land serve only for identification in the computer calculations. An appraiser in a subsequent study might wish to modify certain land ratings where his opinion and knowledge of a ranch differed from the . county classifications. However, the county records for each farm based on the general schedule illustrate.the method of using land classi­ fications and eliminate the necessity of those persons collecting data from making a recheck of each sale,at this time. A question in this study may be raised as to the similarity of,land, classifications between counties. These differences as they exist are expected to fall within a limited range. Sale groups generally are located ,within one county area which should minimize this variance. Part 3. Crop Factors Used to Compute Production Units Of Farms and Ranches The production on crop and range lands may be converted to a common unit in terms of animal unit months of feed. In this study irrigated lands are rate in units of alfalfa hay and dry crop lands in units of wheat to utilize the Montana Land Classification system. Other crops could be considered. The conversion of these crops into AUM's is done by considering the percentage of TDN in the feeding analysis of crops and 28 the pounds of TDN- required for one AUM of feed. Grazing lands may be summed without conversion because they are rated in Acres per Animal Unit Month. References may be found in manuals dealing with farm appraisal which cite the figure of around 400 pounds of TDN■required for one AUM of feed. The following table is taken from the Appraisal Terminology Handbook. 23/ TABLE III. NUTRIENT REQUIREMENTS AND ANIMAL UNITS PER MONTH FOR LIVESTOCK FROM APPRAISAL. TERMINOLOGY HANDBOOK.. Beef Cattle Av. #TDN/Dav. .AU/Month■ Cows nursing for 3 months during year 13.2 1.00 Bulls 13.2 1,00 Yearlings . '9.9 .75 Calves 6.6 .50 Steers, 2 yrs and over 13.2 1.00 The figure developed for this study, with the assistance of Range and Nutrition specialists at Montana State University, is 395 pounds of 23/ American Institute of Real Estate Appraisers, Appraisal Terminology Handbook, Chicago, Illinois, 1961j p. 196. 29 TDN required for one AUM which was rounded to 400. 24/ The method of arriving at 400 pounds of TDN per one AUM is shown in Table IV below. TABLE IV. METHOD OF ARRIVING AT THE-POUNDS OF TDN REQUIRED FOR ONE ANIMAL UNIT MONTH. Livestock Type #TDN/Day Required. Days. Total Pounds - TDN Wintering Pregnant Beef-Cows. 9.0 150 1.350 Nursing Beef Cows 16.8 120 2.020 Remaining Grazing Pd. for Beef Cow 11.0 90 990 Calf (6.4# TDN-@ 400# wt.) Average for 120 days 25/ 3.2 120 385 Pounds of TDN/AUM- = 4745/12 = 395 i 4,475 Rounded.to 400. The figure of.400 pounds of TDN per one,AUM of feed is a key figure in the development of various crop factors which convert production units of the crops into AUM's of feed (see- Table V, page 30). The following example - shows the factor for alfalfa hay and illustrates the general method of calculating other factors. 24/ Welcome assistance was received from Dr. Oscar 0. Thomas, Professor, of Animal-Nutrition and Dr; Gene F . Payne, Professor of Range Science at. Montana State University, Bozeman* Montana. 25/ Wise Burroughs, Chairman, Subcommittee on Beef Cattle Nutrition, Nutrient Requirements of Beef Cattle, National Academy of Sciences-. National.Research Council, Washington, D. C., 1963* p. 2, - 30 - Alfalfa Hay Factor = 2000 lbs, per ton x .50 lb. TDN per lb. of hay 400 lbs. per AUM = 2.5 AUM's per ton. TABLE V. FACTORS USED TO CONVERT PHYSICAL PRODUCTION OF CROPS INTO AUM's OF FEED. Crop Percent TDN 26/ Factor Units Wheat 80 0.12 AUM/Bu. Barley 73 0.09 AUM/Bu. Oats 70 0.06 AUM/Bu. Alfalfa Hay 50 2.50 AUM/Ton Prairie Hay 45 2.25 AUM/Ton The use of land classifications and factors is summarized in the following two examples of sales. These examples serve to illustrate how the calcula­ tions are made by the computer. Example I.— Irrigated Farm Billings— Irr. Farm Sale No. 4 Sale Price Building Contribution Land Contribution Total Acres Sale Price per Acre $16,650.00 600.00 16,050.00 167.00 99.00 26/ Frank B . Morrison, Feeds and Feeding, The Morrison Publishing Co. Clinton, Iowa, 1959, Table I, pp. 997-1069. 31 - Productivity Calculations Acres Land Class A/AUM Ton Alf. Eu. Wht. Per Acre Per Acre Total Tons Total Bu. Factor Total AUM's 66 12 3.7 244.2 2.5 610.5 5 17 1.2 6.0 2.5 15,0 19* F3 14.5 275.5 0.12 13.1 58 Total G4 4.6 Feed Units = 671 .2/12 = 55.9 12.6 671.2 Feed Units Per Acre = 55.9/167.0 = 0.334 Example II,— Livestock Ranch Sale Great Falls— Livestock Ranches Sale No. 11 $90,000.00 0.00 25.71 3,500.00 Sale Price Building Contribution Sales Price Per Acre Total Acres Productivity Calculations Acres Land Class A/AUM Ton Alf. Per Acre Total Tons Factor Total AUM's 3410 G4 3,8 897.1 90 14 2.7 243 2.5 60 7.5 90** Gl 1.5 60.0 1,564.6 * Fifty percent of the total acres of class F3 were used to reflect acres in summer fallow. ** Aftermath grazing available to livestock after hay has been harvested and thus a "G" or grazing category has been used. 32 Animal Units of Range for 7 Months* 957/7 = 136.7 Animal Units of Hay-Year-Lorig 607.5/12 = 50.6 AUM■s of Hay Required for 5 Months 136.7 x 5 = 688.0 AUM's of Hay Short = 688 . - 607.5 = 80.5 AU's of Hay Short = 80.5/12 = 6.7 Total AU on Ranch-Year-Long • = 136.7 - 6.7 = 130 Alternate Calculations Total AU for Ranch - YearTLong = 1564/12 = 130.38 Acres Per Animal Unit = 3500/130.38 = 26.8 Sale Price Per AU = 90,000/130.38 = $690. Since a.numerical conversion factor is used to compute feed units per acre, an equivalent scale may be used which is based on units of crop production. For example, it can be seen in Figure 5 (page.33) that one Feed Unit Per Acre is equivalent to 4.8 tons of.alfalfa per acre. Part 4. Source and Structure of Data Groups To study productivity and other important variables that.influence the.sale;price of agricultural land in Montana, properties were considered to be in three classifications; namely, wheat farms, irrigated farms, and livestock,rancheso In order for a property to bear a particular desig­ nation,, the majority of its land value must have been attributed to the., particular type of land. Thus, if a farm had a combination of land types, the most significant land type in terms of total dollar value would serve to place it into one of the three categories. * The general grazing period for the group of livestock ranches of which this sale was a part.was eight months. This special grazing period is noted in the "AUR" column on the tabulation with an * after "136". See Tabulation Report for Great Falls Livestock Ranches, Appendix B, Page 132. Feed Units Per Acre O .1 .2 .3 „ji .5 .6 .7 .8 .9 1,0 I Equivalent Tons ^of Alfalfa Hay Per Acre I--------'-------H--------1------- 1------1 0 I I 2 3 4 4,8 I I Equivalent Bushfels of Wheat Per Acre 0 10 20 30 4b 50 60 70 80 90 100 Equivalent Bushels of ; Wheat Per Acre— Summer Fallow* I- - - - 1- - - 1- - - - 1- - - 1- - - 1- - - - 1- - - - 1- - - 1- - - 1- - 0 20 40 60 80 100 120 Figure 5, Scales to Convert Feed Unit per Acre Ratings into Crop Production Ratings. * Use this conversion scale if the overall farm rating in Feed Units per Acre is calculated from production of the annual cropped acres divided by total farm acres. Summer fallow acres are not considered as annual cropped acres. - 34 - These three types of properties are found throughout the state but with marked differences between regions. Therefore, it was decided to study each of the groups in more than one area. Records of confirmed sales held by appraisers for the Montana Highway Commission in five state districts offered'a great advantage because they cover the three types of sales throughout the state. These confirmed sales were parts of appraisal reports where particular areas had been studied in detail for the purpose of highway acquisition. None of the sales involved in this study was a sale of property to the Highway Department and all were considered to be bona fide fair market transactions. The use of sales in specific areas was considered to focus attention on the first-hand problems that appraisers in the field face. It was recognized that sales from various appraisers' reports would, have to be brought together in each district to structure groups of sales of the three general types. The entire work of one appraiser had to.be divided into classes because typically he had included more than one, type.of property in his market analysis. Several guidelines were suggested for the purpose of having similarly structured groups from each district. The person in each district who was responsible for compiling the information for this study was asked not to include sales all of one type; i.e., for example, not all large tracts or all small tracts. To achieve some uniformity in bringing sales together as groups, a further condition was that the sales should relate to value in one geographic area. In other words, could a sale be cited as supporting market 35 - evidence for a particular area. To have some reference figure as to the number of sales to be in a group, the range of 35 to 75 sales per group was suggested„ The lower limit was suggested for statistical purposes and the ,upper limit as one which would include the maximum number an individual appraiser would typically analyze in detail. If more.than 75 sales were found for a group, random,selection would be used* However, since appraisers normally consider all sales found to some extent, random selection was not a part of the process until the number would reach 75. It has been observed that appraisers generally place the most credence on sales that have taken place within the past five years. Therefore, emphasis was placed on recent sales; however, sales back as far as 1958 would not be considered too old.. Several problems were recognized at the outset with regard.to the general framework for sales data. First, there wou]_d be. a likelihood of having less than 35 sales in a group. Second, not all five Highway Department Districts would have all th%ee types of sales.. An example of this second problem is the fact that there are very few wheat farms in the western district around Missoula. A number of general variables were considered. An attempt was made to give recognition to variables that would be.hypothesized to be important from a market viewpoint. In all cases Sale-Price per Acre was the dependent variables. Table VI (page 36) is a listing of the variables used in the multiple regression analysis, A variable which was considered but not coded was a measure of the terms of purchase. This is usually an important variable considered by 36 - TABLE VI. VARIABLES CONSIDERED IN MULTIPLE REGRESSION ANALYSIS OF FARM AND RANCH SALES. Variable Label Description Units SP / A Overall transaction price per acre at time of sale Dollars/Acre TIME Date of sale year 1958 =0, '59 I.....'67 = A/AU Overall productivity rating of ranches based on fee land Acres/Animal Unit FU/A Overall productivity rating of farms based on fee land Feed Units/ Acre BLD RATING Appraiser's estimate of buildings 0, 1.....9 TOTAL A Total number of fee acres in sales Acres MI/OIL Miles to nearest oiled road Miles MI/TWN Miles to nearest trade center supplying daily needs Miles PCT L Proportion of total operation of sale on leases or permits (used only for ranch sales) No. Leased Ac: Total Acres or No. AU Leased Total AU ADD ON Was the purchase added to existing holdings Yes = I No = 0 SEVERENCE The degree of severence (used in Great Falls only) 0*1,2,3 - .37 - buyers and sellers. However, judging from pilot studies of data there is a marked uniformity for the standard 29 percent down with the balance over varying periods of time.. A majority of sales were found to have required the standard 29 percent down payment. Only an occasional tract sold for "cash". Moreover terms of purchase include not only down pay­ ment but also period of time, interest rate, etc., which form a composite variable and led to the decision to omit.terms of purchase as a variable. The data included for each farm permitted the breakdown of the . land by type; i.e., grazing, irrigated, or dry farm land with appropriate ratings These ratings were based on the Montana Land Classification schedule with some adjustments. Additional production such as crop clean up could be added where it existed. The data for all sales was submitted on coding forms drawn up for the purpose. of this study (see Figures 8 and 9, pages 5.5 and 56). ' A time factor of 1.00 was used as the sales were processed first without time adjustments. A second pass was made to adjust for time .and compare the linear regression statistics. Sale prices which were not adjusted for time were used as the dependent variable in the multiple■regression model. The effects of time adjustments on sale prices may be observed" in Appendix B and in Tables XII and XIII (pages 76 and 77). Part 5. Linear Regression Model In a study of.the factors which influence the value of farms and ranches, the statistical concepts of regression analysis can be used. - 38 Statistics may be used in predicting a value from market data and in evaluating factors which affect value. The- justification for analysis of data by statistical methods is based on logic. It is hypothesized that the real estate market as reflected by prices is subject to a number of influencing factors. Many factors will be studied by an appraiser who is analyzing a group of sales. Factors believed to be important are studied for all the sales in any group. Various.methods have been used to analyze and correlate a group of market sales. One technique in correlating sales is to construct a simple graph where sale-price per.acre,is placed on the vertical axis and.some other unit of comparison on the horizontal axis. Each of the sales is then plotted to form a scatter diagram. In this manner sale price per acre may be.compared to productivity of the land, distance, from a town, etc. The variable placed on the vertical or "Y" axis is known as the dependent variable and the variable on the "X" axis, the independent variable. In this way sale price per acre is represented as depending upon or related to.some.other factor.. The relationship portrayed in the simple scatter diagram may be studied and analyzed by the statistical technique of linear regression analysis. It is, of course, recognized that generally many factors operate in the real estate market. The study of just one factor might be undertaken if some major factor were to be studied. The statistical - 39 - technique will not,generate cause-and effect relationships but may be useful in evaluating those believed to.exist, In discussing the linear regression model a ranch example will be used. The dependent variable in this case is sale price, dollars per acre, The independent variable is an overall rating of the rapch in terms of acres per animal unit. In this situation sale price per acre is thought to be related to or depend upon the productivity quality of the ranch. The variable, acres per animal unit becomes a factor which may.be used to estimate sale price. In this type of study certain questions may be present at the outset such as how good is the independent variable, acres per animal unit, in estimating sale price; or, is there any correlation at all; or what percent of the price variation can be attributed to the overall productive quality of the land, etc.? A scatter diagram of this ranch example.with a few data points is. shown in Figure 6 (page 40). Each of the numbered points corresponds to one market transaction. A graph such as this,might be used with some success without any statistical calculations. Here, all the sales are compared by a variable common to each of them. This is actually the beginning of the correlation process which is very basic in the appraisal process. The labeling of the plotted points allows the appraiser who-is familiar with each of the sales to spot.other influences such as size, buildings, location, etc. The graph.may become an aid in selecting the most comparable sales for direct comparison to the subject property. — 40 — 30 40 50 Acres/Animal Unit Figure 6, Scatter Diagram Illustrating Correlation of Sales Graphically. From the scatter diagram it may be desirable to estimate a trend relationship. A trend line that represents the data as a whole could be placed on the graph by sight. In this hypothetical example, a line sloping downward to the right would come closest to most of the points. Some of the attributes of such a scatter diagram and trend line may be evaluated by the statistics of linear regression analysis» The best fitting trend line may be derived mathematically by the method of least squares = Such a line is called the regression line„ An estimate of the sale price per acre for a ranch could be obtained by knowing the overall acres per animal unit factor, going up to the regression line and then reading the corresponding priceo — 41 — This linear relationship is hypothesized to exist. The true best fitting trend line may not,be linear. A linear relationship or linear trend line may.be represented most simply by the mathematical.equation Y = a + b X. Here Y is the dependent variable, sale price per acre and X the independent variable, acres per animal unit, When the constants a and b have been determined, the,sale price per acre may be estimated by substituting into the equation the particular value of X; The constant a is the point where the regression line intercepts the Y axis and the regression coefficient b, is the slope of the regression line. The linear estimating equation has the form Y'-= a + b X where Y' denotes an estimate of Y based on X. An estimate may be.made for a sale in the group of sales or for a subject property not in the group.* It would be extremely unlikely that all the points in.any scatter diagram would lie along the regression line. However, the better the fit of the points along the line, the greater the reliance we would be inclined to place on this estimating procedure. Since,no group of sales is ever expected to perfectly fit a regression line, some consideration should be given.to some of.the statistical tests and measures that may be a,guide for the amount of reliance placed on the estimating equation. It is also important to consider.sample error. A group of,sales is considered to be a representative number of all the farms or ranches in a particular area. Some.of the tests and.measures are.discussed as follows. *A method for calculating the constants,a and.b is shown,in Appendix1A, page.103.. — 42 — Standard Error of Estimate As can be seen from Figure 6 (page 40), not all price difference was accounted for by one variable„ Thus, error in the estimating procedure is considered to exist= One■measure of error is the standard error of estimate. Graphically this may be thought of as a band above.and below the regression line = The standard error of estimate is computed in such a manner that 68 percent of the time, the true estimate of the value will be in the banded area. Similarly by use of a "t" table, a 95 percent confidence interval can be established. If the standard error of estimate in the ranch example was $20, and the predicted value for a particular ranch $45 per acre, then it would be expected that 68 percent of the time the true value for this ranch would be within the range of $25 to $65. The standard error of estimate may be,illustrated using data.of the hypothetical Figure - (page 40) of ranch sales. This banded area is shown in Figure 7 (page 43)= Thus, for any estimate made with the regression equation, the estimated sale-price per acre needs to be accompanied by the range, given by the standard error of estimate. Coefficient of Determination and Correlation The strength of the relationship between the independent variable and dependent variable may be evaluated . Because - it is recognized that acres per animal unit is only one factor affecting the sale price per acre, it may be desirable to have an idea of the percent of the price which this factor explains. The- coefficient of determination (r%) has 43 - Sale Price $/Acre Figure 7. 30 40 50 Acres/Animal Unit Illustration of Standard Error of Estimate in Simple Regression Analysis. been developed to show what proportion of the original variation in sale price per acre has been taken into account. 27/ In the ranch example, a coefficient of determination of r^ = 0.65 indicates that 65 percent of the difference in sale price per acre may be accounted for in the dependent variable, acres per animal unit. This leaves 35 percent unaccounted for which might lead one to believe that the major influence in sale price per acre had been determined. However, this does not in itself imply that differences in sale price per acre were caused by carrying capacity differences. It has been stated that, 27/ " . . . the coefficient of determination (r ) shows what proportion of the variance in the values of the dependent variable can be explained or estimated from, the con-comittant variation in the values of the independent variable." Mordecai Ezekiel and Karl A. Fox, Methods of Correlation and Regression Analysis, John Wiley and Sons, Inc., 1959, New York, p. 147. — 44 — The statistical measure merely tells how closely the variance in one variable was associated with variance in the other; whether that association is due to, or can be taken as evidence of, cause-and-effect relation is outside the scope of statistical analysis. 28/ The value of (r^) varies from 0 to I. Since this is a ratio, it is expressed as a pure number. An index for measuring the closeness of fit of the points about, the estimated line of regression is the correlation coefficient (r). 29/ Numerically (r) is the square root of the coefficient of determination (r^). Thus,' it may range in value from -I to I. The value of (r) will be higher (absolutely) if the points are located near the ends of the line and there is a small scatter. If most of the points are located near the middle of the line and have a large scatter, (r) will be low in value. 30/ The sign associated with (r) is positive if the regression line slopes upward and negative if it slopes downward. It has the same sign as b in Y ' = a + b X. Regression Coefficient The regression coefficient b in Y' = a + b X is the slope of the regression line. The true regression coefficient for the population of ranches, B , is estimated by b. Some statisticians in recent years have placed more emphasis on the regression coefficient than on the 28/ Ibid., p. 139. 29/ Jerome C. R. Li, Statistical Inference I, Edwards Brothers, Inc., Ann Arbor, Michigan, 1964, p . 301. 30/ Ezekiel and Fox, op. cit., p. 129. - 45 - correlation coefficient (r). 31/ The slope of the regression line indi­ cates how many units Y change for a unit change in X. The slope appearance will depend partly on the scale of the graph. A horizontal line with slope of 0 where b equals 0 shows no dependence of the variable Y on the variable X= A modest slope shows that the dependent variable does vary with changes in the independent variable. A vertical line also indicates that the independent variable does not influence the dependent variable. Standard Error in Regression Coefficient The regression coefficient is not without possible sample error. Since the regression equation is an estimate from a sample of the whole population of ranches in an area we can accept or.reject on a probability basis whether or not the true regression coefficient is equal to any value. The' usual hypothesis tested is that the true regression coefficient B, is equal to 0. If it can be concluded that the true regression coefficient is not equal to 0, then a significant relationship exists between sale price per acre and acres per animal unit. To make this test, the statistic t = (b-B)/S^ is computed which employs the standard error of the regression coefficient, S^. A graphical interpretation of the standard error in the regression coefficient may be thought of as a plus and minus slope change 31/ Ezekiel and Fox point out,that the regression coefficient b is the same regardless of whether the X,values are drawn at random or are subjected to purposeful selection.' Correlation is more, important, where both the X and Y values are drawn at random from a bivariate normal universe. ■ Ibid., p. 130. - 46 - in the regressiqn line where the pivot points is at X; Y* on the regres­ sion line. The estimated error of b does not depend entirely upon sample size. The spread of the X values is also important. 32/ Hypothesis Testing The statistic t = (b-B)/S^ follows the t-distribution, for samples sufficiently large. This statistic has n-2 degrees of freedom allowing for the calculation of the parameters a and b. In this case, B = 0 is our null or basic hypothesis. Thus, t = b/S^. This is what is referred to often times as the T-ratio. The alternative hypothesis then is B ^ 0. The test is normally a two-tailed test. A test for significance at the 95 percent** level implies then that 2.5 percent be placed in each tail of the t-curve, From t-tabIes the critical value of t ,may be obtained. If the absolute value of the calculated t-ratio is greater than the critical values of t, the null hypothesis is rejected. The alternative hypothesis that B f 0 is accepted implying that there is a significant rela­ tionship between the two variables. If it is known beforehand that the true regression coefficient can only be positive or negative, a one-tailed * The mean or average of the X values is noted as X and similarly for the Y values, Y. 32/ Li, op. cit., p . 320. ** A significance level of 95 percent implies that there is less than one chance in 20 that the population of ranches from which this sample was drawn does not have the positive association of sale price per acre with acres per animal unit. In this ranch example, the association is considered positive in spite of the fact that the regression line is negatively sloping. — 47 — test can be made. Here a test at the 95 percent level would place 5 percent in one tail. 33/ Summary A brief discussion of concepts in the linear regression model has been made for two purposes. First, linear regression analysis may be able to help an appraiser evaluate a particular market relationship. Second, the linear regression model with its graphical representations is useful as a basis to begin a discussion of the multiple linear regression model. Besides the assumptions that statistics and regression analysis require with regard to the manner of data selection, sample size, normal distributions, etc., some other problems may arise where this technique is applied. One such problem is the case where two groups of data are put together for an attempted analysis. Such a case might be where a group of adequately watered ranches was being compared with a group of poorly watered ranches, If the ranches were apparently grouped high and low on a scatter diagram, a regression line through the middle would be virtually meaningless, To a scientist or an appraiser the lack of association between two variables may be just as important as knowing of a positive association. In the ranch example if the regression line were horizontal implying that sale price per acre was not related to land quality as measured by the 33/ Li, op. cit., p. 322. — 48 — variable acres per animal unit, an appraiser would be led in his analysis to study other factors more closely and disregard land quality in compari­ sons. Information of this type is very important to any appraiser who is involved with market value appraisals such as mortgage loan appraisers, highway right-of-way appraisers, or estate appraisers. The example of ranch .sales which has been used to illustrate linear regression analysis has considered only one independent variable namely, acres per animal unit. Since this is a composite variable measuring the productive quality of a ranch it might be thought at the outset to be an important one. However, the same type of graph could be constructed using other independent variables. Part 6. Multiple Linear Regression Model Multiple linear regression analysis is a technique whereby an esti­ mating equation can be developed through the consideration of more than one independent variable. 34/ The extension from the simple linear regression concept is a logical one because normally many factors are considered to influence real estate values. The estimating equation has the form Y' = a + b^ X-^ + b^X^ + b^X^ + . . . + b^X^. In this equation the X's represent relevant facts about the property. Y' is the estimated or predicted value such as sale price per acre and 34/ Two references which may be consulted on the subject of multiple. regression analysis are: Mordecai Ezekiel and Karl A. Fox, Methods of Correlation and Regression Analysis, 3rd Ed., 1959, John Wiley and Sons, Inc., New York, and Robert G. D . Steel and James H. Torrie, Principles and Procedures of Statistics, McGraw Hill Book Co., Inc., New York, 1960. - 49 - the constant term "a" is the value when all.the X factors are zero. The regression coefficients ... are net regression coefficients; they are unbiased estimators. Thei term net regression coefficient is used because each indicates the amount of change in the predicted value for a one.unit,change in the variable when other things are held constant. In the section on Linear Regression Analysis an example was used for illustration purposes relating to ranch properties. This example showed sale price per acre related to the overall ranch productivity rating, A/AU. This model,can be extended to include other independent variables. A second independent variable such as miles from an oiled highway could be added to the estimating equation. Similarly, other factors could be added. Some;factors may be conceived to be important in influencing price but may be found to be unimportant after an evaluation. For a,group of variables it may be desirable also to have some idea about the importance• or rank of the variables considered. Tests and computations may be made to yield this information along with some other measures that may be useful in evaluating the multiple regression model. A first.consideration for evaluating multiple regression results has to do with sample size.. It is somewhat intuitive that less confidence should be placed on small'samples than on large samples. It can be shown that some,of the statistics such as coefficient of correlation, coefficient of determination, and standard.error of estimate are biased up or.down,for cases.of small samples. 35/ 35/ For a discussion on small samples see Ezekiel and Fox, op. cit., pp. 300-304. 50 - 2 2With .a small sample.r or R tends to overstate the amount of variation in the Y or dependent variable which is explained.by the X variable (s). To overcome ,this bias, an adjustment must be made for the degrees of freedom. The degrees of freedom may be considered as the number of variables that are free to vary. The number of degrees of freedom is the number of observations in the sample less the number of constants in the regres­ sion equationo An example of computing the number of degrees of freedom may be drawn from a multiple regression problem in which there are 40 observa­ tions and,3 independent variables. The number of degrees of freedom is 40 - 4 or 36. If a sample had two observations, a straight line could be perfectly fitted through the two points. Other observations could be added,in■such a manner that no correlation was revealed. The line described by the two original points could not vary; it was fixed. There exists no degree of freedom. Thus, it is apparent that reliability decreases as the number of degrees of freedom is reduced. Some of ,the statistical measures which may be useful in evaluating multiple regres­ sion results are discussed as follows. Standard■Error of Estimate The concept of the standard error of estimate is similar to that for the linear regression model in that it is expected that 68 percent of the time interval of plus or minus one standard error will contain the true value. Since the equation is multidimensional it is not graphed nor banded like the simple linear model. 51 - Coefficients of Multiple Determination and Correlation The coefficient of multiple determination (R^ ) gives an indication of the amount of variation in the dependent variable which is explained by the independent variables in,the model. Similarly, the coefficient of multiple correlation (R) is a measure of the linearity of the model. For small samples, the true R could be considerably lower. As an example, an R of 0.90 for a sample of 15 observations with 3 independent,variables could have a probable minimum as low as 0.70. It is possible to have I sample out of 20 which would show as high an R as 0.90 but have a,true, value of 0.70. 36/ The probable true value decreases as the number of variables are added for a given sample size. A sample,size of 100 would not be expected to overstate R by more than 4 percent for up to,7 inde­ pendent variables. Coefficients of Partial Correlation A correlation between the dependent variable and any other one, variable.in the multiple regression equation may be vindicated by the coefficient of partial correlation. The'other independent.variables are considered to.be held constant or.their effects,removed. An inde­ pendent variable may have a weak correlation with the dependent variable in simple correlation by being masked by the effects of other variables.' Yet this same variable may show a strong partial correlation. 36/ Ezekiel and Fox, op.'cit., pp. 293-300. - 52 - Net Regression Coefficients Net regression coefficients of multiple linear regression take on special importance. Each coefficient indicates how much the dependent variable is expected on the average to change for a one unit change in one independent variable, with other variables held constant. An equa­ tion of Y = 65.63 - .70X^ - 3 . for the ranch example where Y is the estimate of the sale price in dollars per acre, X^ is the variable A/AU* and X^ miles from town illustrate these points. For every mile from town, $3.38 per acre is subtracted. Such an interpretation is only valid over the range of the distances which the sales in the sample were from town. It may occur that at times the sign will appear wrong in an equation based on what would be expected. If a positive sign is associated with miles from oiled highway, where it would be logical to expect higher values along the highway, one problem that may exist is that of multi- collinearity. In other words, this variable may correlate closely with some other variable. A second reason for the wrong sign appearing may be that the variable itself does not test significantly different from zero. Significance of Partial Regression Coefficients The partial net regression coefficients are not.without error. This error is called the standard error of the net regression coefficients and tested by the "t" test. The "t" statistic is calculated in a manner similar to that in linear regression. However, one distinctive feature is the adjustment for the degrees of freedom. To determine if a - 53 .- significant relationship exists, the calculated t value should exceed the value from the t table» The value in the table is for a given level of significance and.n-m degrees of.freedom., Here n is the sample.size and m is the number of constants in the regression equation. It can be readily seen from a t table that for any given level of significance the required value for t to be significant decreases with the number of degrees of freedom. The error in the partial net regression coefficient is usually noted as . Standard Partial Regression Coefficients One method for studying the relative importance of the variables included in the multiple regression equation is by comparison of the standard partial regression coefficients. The partial regression coefficients, b ’s in Y 1 = a + b-^ x^ + + ... + bnxn are,in particular units of measurement. A comparison of the b's will not give a rank of their importance.. However, standard partial regression coefficients are in the same units, standard deviations. ' These may be determined from the partial regression coefficients (bis) from the general formula: bi(si/s^ ). 37/ Here refers to the standard deviation of variable.I and. s the standard deviation of the dependent variable.. In some cases the y rank of the.variables by this comparison may be similar to that shown.by a ranking of the partial correlation coefficients. However, this is not always true. 38/ 37/ Steel and Torrie. op. cit., p . 299. 38/ Ezekiel and Fox, op. cit., p . 197. 54 - Part 7o Computer Processing of Data The great advantage offered by the computer is speed., Basically, its operations are the same as would be done by hand. Each operation must have been given to the machine in a set of pre-programmed instructions. The particular computer on which this data has been processed is the IBM 1620 - Model TI computer on Montana State University Campus. Data is read in on cards and output information is either printed by an on line printer or punched on output cards which are later interpreted and printed. Therefore, the field coding forms were devised in such a manner as to allow direct key punching of'data onto cards. The data are processed by several'programs. The data tabulation program, linear regression analysis program, plotter program and the program for computing the predicted sale prices were written especially for this projectd The multiple regression program is one that is available at the Montana State University Computing Center. 39/ Field■Coding Forms The field coding forms were written so that all.data, would appear columnized (see Figures 8 and 9, pages 55 and 56). Two cards are necessary to contain the data used for each farm or ranch. Thus, the top corresponding line on Page B is a continuation of the top line on Page A. These data are then transferred to cards through the key punch and put in proper sequence. 39/ Glenn Ingram, "One Pass Multiple Regression Program", Montana State University Computing Center. Sale Group Type, Check One SALE DATA CODING FORM - PAGE A I Irr. Farms I I Dry Farms Livestock I Project Page__________of______ Pages t*eo '---- ‘ '----- -----lRanches ---- * Report o 55 *Ose when available _______ **At least 1.00_______ ***For Livestock ranches only________________________________________ _ Xi Ijajj Grantee Il SalePrice * , Assessed Value itme Factor Building Value Total Acres Annual Income ***Grazing Period Mi. to Oil Hwy. Ml. to Town Yb Ili Examples i I i i i i i i I I I i* Iiiii i I* I'I I I I I .1 I I* i L I i I I I 11*1 I -I-1-1*1 ■ ■ .»i *i I i I I JlOiW, , I , I ♦ I ,9.^ *,a,*. , ,3,ct 4^4. /,.,40 I J tQ O P P t. i i vVx93X- 3C I 1 M 1 I 3H3X- P . . . I I X Yb  b  b I i4,^ *U&2 Pr i I i i * Ifit. P O .I6t.fi 3,7,. bfi¥ i I I ' * f ' ' ' ' I ■ I I _L_ < 111 iii* 3A3 P UL i i i i 11» I I * I I LI I I I I i I I 1*1 I I I I*, I I I I I I I I I I I -L * I I I 1-4 if ■ 1111 * ■ ♦ I"* i M 1 1 i i* I I * I I I*‘ I M i l l I # I | 1*1 I I l#f I I I I I I I { I I I I I I I m I I I I * I * !• I'l i _L 3 3 3 3 I i* I III I 1*1 I I 1*1 I f I 1*1 I i i i i t i i I 11 - U I-I-I 1111» 3 3 3 3 » I i» i'i i I 1111 ■ i* I III I I'I I Illll I * I 1*1 I i I i« I * i i ■ 11 I l I l L L J-U- - L iiii I 11* I I i I I If* n i -L Li*. I I I I I LI I Illll un I 1*1 I I I l*| I I I* I B I i I I I ■ < I I I' I I-I. I I I I »* 1 1 1 1 4 1 1 » I*1 1 —L. -Uti I I I I I * I I I I I I * I* I I I I fel I I I* I   f • I I I I I I I I I I I I I I i i i i i i i' IIItlIl,* in I I Iiii I I* * I I I I I'I I Illll I 1*1 I I I  I Illel  f I I I I I I 1 1 1 ill. u I I i I ill* i*i i i l M I I I I * u n u Illlf I 1*1 I I I 1*1 I I I I I I I I ■ I i m I i I  I  i* iiii I 4.C. P 3T3 i Im I I* I III I I* I * * 1*1 I I i i'i i l**i B I I I I I I I I I I *   IIII I II* i * i I -ii —i-1 I I* I I 4 I I 1*1 * 11*1 I I I 1*1 u I i*i  i I *        I I I III. I I I  i*i I I     I I* i i i i I |»i I * I f*l I I I 1*1 I I i*i  \ * I   * * I * I * I I I IJ- m I i * I I I i* I * * * I I u n i I       * I I I i* I I' I 1*1 I I I 1*1 iil#i B i i I I I I I I * I I I I    I * iV I I I I. I I I*    m * m u I I* * I I I I 1*1 * *     I* I 1*1 I I I 1*1 Iliei B I I * * * * * * * *I I I I Illl I I I*. 1*1 I I m m   I   I III li*i   I 1*1 I i i 3T3 I I i*l B I I * * I I I  I i I I I I  I I  iii» * *  u 1 I I I * *  *       I I 1*1 I  I  I * * *   B i I Al * I III I-ill- -L I I I I I I I*  I I i ill*  *  * * mm  m  I 1# I Illll*! -L I I I I I *   1*1 I I I l»l i.i ifi #i I i * I I Ui Ui * Figure 8. Coding Form to Record Raw Sale Data— Page A. SALE DATA CODING FORM PAGE B Sale Group Type, Check One I Irr. Farms | ] Dry Farms | | Livestock | | Project Page of Pages Ranches Report Use Up to 8 Types of Land Per farm in any order Examples of Entries Range Land Irr. Crop Land es ! 475. ss "I" class ! I Id, Ton Alf./A =4.5 Dry Crop Land Acres ! 876. Class ! " # " Subclass ! 2 Yield, Eu. Wht/A ! 24.0 .4. 0.0C 6 S ,7,7 Class ! "G" Subclass ! 5 Acres/AUM ! 7.7  '  $  Cla I   % p f, F ZLfliC Sub Yie * * *    * *     * *     * * * * * * * * *  *  *  * * * *   * * *  m * * *  * *    *    * * * * * * * * * * *  *    * * * * *    * * * * * * * * * * * * * * * * * * * *    *     *    *    * *   * * *    * * *    * * *    * * *    * * * *  * * * * *  * * *      *  B * * *   * * * * *    * * * * * *   * * * * * * * *  * * * *    * * * * * * * * *    * *  * * * * * * * * *   m m * * *    * * *    * * *       *    * *   * *   B * *      * * * * * * *    * *   * * *    * * *    *  * * * * *     * * * *     * Il *    * *     * * *    * * *    * * *    * * *    * *   * * i L-Li *  *    * * *    * * *    * * * * * * * *   * *    * * * * * * * *    *  * * *    * * * * * * * *     * * *    * * *    * * * *  * * * *    * * *    *    * * Illl * * *    * *     *  *    * *    *  * *    * * * * * * ■    * * * ■ I & I * * * * * * *    * * * * * * * * *    * * * * * * * * *    * * *    *    * * IlIllM * * *    * * Figure 9. Coding Form to Record Raw Sale Data— Page B 57 Page B recorded the various types of■land found on each farm and their production rating. Up to eight kinds of land could be entered in any order. The processing of the raw data by the tabulation program included punching out cards with the appropriate data for the multiple regres­ sion program and plotter programs. Thus, by including all the data.on the first set of cards, the need to key punch a second set of cards was eliminatedo For programming efficiency the headings of the columns in the tabula­ tion reports were abbreviated. In most cases,these abbreviations are at least somewhat indicative of.the data represented. The complete descrip­ tions for the columns with the corresponding abbreviations are shown in Table XXIII (page 107) at the beginning of' Appendix B , One-Pass Multiple Regression Program The one-pass multiple regression program allows for a great deal of flexibility. Any combination of regressions may be run as a problem. A total of 30 variables may be read in for consideration. Any variable may be designated as the "Y" or dependent variable,, along with the particular X's which are to be.included,in the regression problem. The first part of the output lists means, standard deviations, vari­ ances and sums of squares. A correlation matrix follows which is one,of simple,correlations.of all variables. For each problem a note is made of which variable is the ."Y" variable and the B , SB, T and partial correlation coefficient associated with each of the X’s included in the problem. The "0th" X is the constant term of the multiple regression equation and is listed under the column headed by "B". Also included, are several other statistics about the model and the analysis of - 58- variance table. CHAPTER- V DATA PROCESSING RESULTS The general areas of Montana from which sales data were obtained may­ be seen in Figure 10 (page 60). Each district had groups of wheat farms, irrigated farms and livestock ranches except the Missoula District. Not enough wheat farm sales were available in any one area to form a wheat farm data group for the Missoula District. A short description of each of the sale data areas is given below for the purpose of assisting the reader in interpreting the results of this study and visualizing the particular localities. Billings Irrigated Farms . A.total of 32 sales were analyzed from the Huntley-Ballantine area which is located approximately 20 miles northeast of Billings in the. Yellowstone River Valley. This area surrounds the proposed line of Interstate Highway 94 and present U .S. Highway 10. The soils of the area are typically river bottom alluvial soils which grade medium to heavy. Alkali is a soil problem as is poor drainage in some areas. Although Billings is growing to the east and west, there.is less develop­ ment in the way of ,urban expansion toward the east or northeast along the Yellowstone River Valley. Irrigation water is delivered by canals from the Yellowstone River. Billings Wheat Farms A small sample of six.sales were analyzed from the area between Columbus and Joliet, some 40 miles west of Billings. These.sales were GLENDIVE MISSOULA *''( BILLING MONTANA Wheat Farms Livestock Ranches Irrigated Farms Project Report Area Figure 10. District Areas of the Montana Highway Commission and Source Areas of Sale Data 61 - typical rural, dryland farms. Grain may be marketed in Columbus, Joliet or Billings at local elevators. All the farms in this group would be classed as upland farms with some hay or range land interspersed. The principal crops produced are winter wheat and barley with generally one- half of the land summer-fallowed duripg the year. Because of sample i size it was difficult to apply regression analysis statistics. Billings Livestock Ranches There were 23 livestock ranches studied in the vicinity of Ryegate. This general area is 29 miles east of Harlowton and 62 miles northwest of Billings. Nearly half of the sales were small tracts of grazing land purchased to add on to an existing ranch. Most of these add-on tracts were grazing land only and did not contain hay land. The larger ranch unit sales generally contained a set of improvements. The typical opera­ tion in this area is plains ranching. Very few of these ranch sales involved any leased lands. Butte Irrigated Farms A sample of 34 irrigated farms was analyzed from the Belgrade area. Since this area is only 10 to 20 miles from Bozeman and Montana State University some urban influence is expected. The advent of the constructed interstate highway in this area which closely parallels old U, S. Highway 10 has not altered access to towns or markets in any appreciable degree. The general area is considered to be a part of the Gallatin Valley. The soils generally are silt loams,fertile* and of alluvial origin. These soils vary from shallow to deep. Irrigation water comes from the 62 - Gallatin River or its tributaries and is distributed by gravity flow. Only four of the farm sales in this group were purchased as add units. Butte Wheat Farms The group of 17 dry land farms in the Butte District came from an area north and south of Towns end. Generally these sales were located in the valley of the Missouri River or in the low lying foothills on either side of the valley. Most of the soils would be classed as upland or bench soils. About one-fourth of all the sales in this group were considered as add-on units. The principal crops produced are winter wheat and barley where generally one-half of the land is summer-fallowed during the year. Butte Livestock Ranches A total of 22 ranches from the Dillon-Melrose area were studied. The headquarters for ranches in this area are typically in the valleys or foothills. Frequently a ranch operation will include the grazing of livestock on government land on a permit or lease basis. The period of grazing the range land is typically seven to nine months. The cattle are wintered on hay and aftermath grazing in the low meadows. Hay is raised on sub-irrigated and irrigated lands. Irrigation water comes from local rivers or mountain Streams. Glendive Irrigated Farms Fifteen irrigated farms within 20 miles of Malta were analyzed. These farms are located along the Milk River valley. Irrigation water 63 - has its source in the Milk River with water being spread by gravity on farms. The soils generally are medium to heavy alluvial loams and clay loams. These farms are located along U. S. Highway 2 or within a few miles of the highway. Crop production includes alfalfa hay, grain, and irrigated pastures. Glendive Wheat Farms The 33 dry land farms studied in this district were located in the spring wheat area of northeast Montana near the towns of Plentywood, Scobey, and Poplar. The soils are typically glacial till loam with some stone interspersed. This area is one of general wheat farming although there are scattered livestock ranches and range lands. These sales came from an area which is on the western edge of the Williston Basin. The oilfield north of Poplar has a number of producing wells which have been developed over the years. Other oil developments have included the Tule Creek field north of Wolf Point and wells in the Medicine Lake area. However, for most of the area the mineral rights have been sold from the land. Thus, the land market today'is not appreciably affected by oil activity. The principal crops produced are spring wheat and barley with one-half of the land summer-fallowed during the year. Strip farming is the general land pattern. Glendive Livestock Ranches The group of 12 livestock ranch sales analyzed from this district are located within 20 miles to the northeast and southeast of Malta. This is an area of plains ranching. This group of sales was about half - 64 - add-on units. The topography is typically rolling hills.. Only sales Numbers Seven and Eight had any leased land in connection with the purchased acres. Great Falls Irrigated Farms A total of 13 irrigated farms were studied in the vicinity of Harlem and Chinook. These irrigated farms, located along the valley of the Milk River, are very similar to the irrigated farms in the Glendive District some 25 miles east. Irrigation water is derived from the Milk River and mostly distributed by gravity flow. There is a small amount of sprinkler irrigation. The soils are typically medium to heavy loams and clay loams. Great Falls Wheat Farms The group of 33 wheat farm sales are.located on the eastern edge of the golden triangle winter wheat area just north and west of Fort Beriton. The topography varies from gently rolling to level. The soils are generally medium loams to heavy loams or gumt?o. Some rocks are inter­ spersed in the topsoil as this is an area of Wisconsin age glacial till. Strip farming and block farming are practiced. About one-third of the sales in this group were add-on units. These sales generally had small amounts of range land although they were principally producers of dry land grain. The principle grains produced in this area are winter wheat and barley with typically one-half of the land summer-fallowed in any given year. Great Falls Livestock Ranches A total of 21 livestock ranch sales were studied from the Wolf Creek area 40 miles southwest of Great Falls. This area is one of general ranching with mountain range areas and valley hay meadows. This group of sales was nearly three-fourths add-on purchases. Sales Numbers Five and Seven were much larger in size than the typical sale in the group of 2,000-3,000 acres. A majority of the sales included substantial acreages of hay land. This area has experienced a large demand for recreational acreages and cabin sites along drainage ways. '-Mi'ssbuTa-'Frrigated Farms ' • / • '' " " : , . Thirteen irrigated land sales were studied in this district from the Hamilton-Lolo area. These farms are located in a mountain valley and derive irrigation water from rivers and mountain streams. There is some urban influences in this area which begins south of Missoula as typically people live on properties in this area for rural homesite purposes and commute to work in Missoula. The soils are generally alluvial, glacial, or lake bed soils of a medium sandy loam or loam with rock interspersed in texture. Missoula Livestock Ranches This group of 14 range land sales came from the Bearmouth-Flint Creek area about 35 to 50 miles east of Missoula. This area is one of mountain range land and valley irrigated and sub-irrigated land. In general, the valley is narrow. About one-half of the sales were add-on — 66 — purchases. In general the purchases in this area are small acreage-wise with the average sale size being 774 acres. This is an area where out- of-sate buyers are an important segment of the market although nearly all of the sales analyzed in this group were to local operators. Summary of District Areas Table VII (page'67) shows a number of comparisons of the sales studied. The figures illustrate some of the differences that exist for sales of similar types in different areas of the state as well as showing some common trends. From this table it can be seen that the average size sale varied in different parts of the state. A large proportion of the sales were add-on's throughout the state. The amount allocated for building contribution value per acre varies but has a reasonable degree of uniformity for particular types of sales. The information in this table illustrates similarities in the land market throughout the state and similarities in the independent analyses of the market by individual appraisers . Productivity comparisons of the groups of sales may be seen in Table VIII (page 68). The average productivity for each of the groups of sales is quite uniform for the type of sales as a whole. The feed unit per acre rating of the irrigated farms ranged from 0.278 to 0.467. For wheat farms the range was 0.060 to 0.086. The acres per animal unit variable for livestock ranches ranged from 18.013 to 44.016. Those ranch sales in the lower part of the acres per animal unit range were sales with a relatively large amount of irrigated or sub-irrigated hay ; land. The sale price per feed unit for farms displayed a wide range yet TABLE VII. COMPARISONS OF SALE GROUPS IN DISTRICT AREAS— PART I. Group Type District N Average:Percent: Size : Add-On: Acres : Sales: Average Bldg. : Contribution : Per Acre Per : Unit of Bide.* *: Average Sale Price Per Acre Irr. Farms Billings 32 118. 37.50 $ 24.80 $ 216.76 Butte 34 268. 11.76 23.97 261.30 Glendive 15 181. .06 20.08 118.64 Great Falls 13 278. 0.00 * 104.32 Missoula 13 185. 23.07 4.81 248.84 Wheat Farms Billings 6 513. 66.66 11.03 57.82 Butte 17 351. 23.52 1.64 116.63 Glendive 33 391. 39.39 .95 69.62 Great Falls 33 553. 30.30 * 55.25 Livestock Ranches Billings 23 1463. 47.82 15.41 25.10 Butte 22 2631. 40.90 4.85 52.95 Glendive 12 1304. 49.99 .82 25.40 Great Falls 21 4326. 71.42 * 34.97 Missoula 14 774. 49.99 8.41 64.83 * Building contribution value not available. **Building contribution is based on a rating of 0 thru 9 with 0-3 for minimum buildings, 4-6 for average buildings, and 7-9 for superior buildings. Thus, in the Billings Area a farm with minimum buildings rated at I would have a building contribution of $24 per acre. TABLE VIII. COMPARISONS OF SALE GROUPS IN DISTRICT AREAS— PART II. Group Type : District N . Ave. S.P.VA : Ave. :S.P./FU : Ave. :LV/FU Ave. FU / A : Ave. :S.P ./AU : Ave. : A/AU : Ave. :Assess-Sale : Ratio Irr. Farms Billings 32 216.76 603. 526. .375 _ _ _ _ .16 Butte 34 261.30 1010. 909. .316 — — .20 Glendive 15 118.64 327. 271. .385 — — — G. Falls 13 104.32 251. 251. .467 — — — — Missoula 13 248.84 1146. 932. .278 — — — Wheat Farms Billings 6 57.82 791. 615. .084 — — — — .29 Butte 17 116.63 1448. 1238. .086 — — .18 Glendive 33 69.62 1157. 1138. .060 — — — — — G. Falls 33 55.25 730. 730. .078 — — — — Missoula 0 Lvs tk. Ranches Billings 23 25.10 — — — — 877. 44.016 .19 Butte 22 52.95 — — — 1008. 24.48 — — Glendive 12 25.40 — — — 728. 40.646 — G. Falls 21 34.97 — — — 572. 18.013 — — Missoula 14 64.83 — — — 1116. 25.75 — — - 69 - correlates with the average sale price per acre. The sale price per animal unit for ranches appears reasonable for the type of sales studied and the manner in which carrying capacities were computed. A sale price per animal unit would be expected to be higher for smaller, add-on units dr if the carrying capacity was conservatively estimated. Tabulation Reports A tabulation of the basic information pertaining to each group of sales is shown in the pages of Appendix B . This type of report offers a summary of some of the important numerical facts about each sale. In addition the statistics regarding the linear regression analysis of the sale price per acre variable and productivity variable have been printed. The merits of using this type of report and a computer to make the calculations becomes more apparent with the larger groups of sales. The format of the livestock ranch reports indicates to some extent the relative amounts of animal units during the grazing period (AUR), the year long animal units of hay (AUH), and the total animal unit carrying capacity of the ranch (AUT). Linear Regression Statistics Some statistics usually considered in simple linear regression analysis have been printed by the computer on the tabulation reports. A summary of these statistics can be seen in Tables XII and XIII (pages 76 and 77). The essential difference in the information contained in these two tables is that in Table XII the sales were not adjusted up to 70 - date for time. It is worth noting that the model tests statistically significant for all groups of sales with the exception of the Billings Wheat Farms group which was a very small sample. The r terms for the time adjusted sales were only slightly increased for 9 out of the 14 samples. However, the time adjustment appears to be more important in influencing the position of the trend lines of the data. The trend lines can be seen to be shifted upward generally for all the sales. See Figures 11, 12 and 13 (pages 71, 72 and 73). The uniform pattern of the trend lines which can be seen in these graphs with the particular area differences being demonstrated also, adds support to this type of analysis. Time Adjustments of Sales Prices Time adjustment of sales was not made on the first pass of the linear regression analysis. However, an attempt was made to observe the effects of considering time adjustments. The time adjustments used for sales occurring prior to 1966 were computed from U.S.D.A. statistics for Montana. 40/ The index figures for sales price of Montana are shown in Table IX (page 74). From these index figures an adjustment of 4.0 percent for irrigated land, 4.75 percent for dry farming land and 5.8 percent for range land per year was calculated. The rounded figures of 4 percent, 5 percent and 6 percent were used in computing the annual time adjustment. The method for computing the percent change in price per year is shown in Table X (page 74). 40/ Economic Research Service, U . S. Department of Agriculture, Farm Real Estate Market Developments, Washington, D . C., July 1966. 550. 0 — — i » i t S I I i « i I I I I I I ___.__________^ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 , _ , Feed Units/Acre Figure 11. Graph of Linear Regression Trend Lines for the Groups of Irrigated Farm Sales by Districts and All Districts Combined. 1251- °l_ O Figure 12. ^ i J i i _____________ i______________ I______________I I______________i______________I 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 Feed Units/Acre Graph of Linear Regression Trend Lines for the Groups of Wheat Farm Sales by Districts and All Districts Combined. loot O -- O Figure 13. 4 | I I I i > i I ■ i t i t IO 20 30 40 50 60 70 Acres/Animal Unit Graph of Linear Regression Trend Lines for the Groups of Livestock Ranch Sales by Districts and All Districts Combined. I W * 74 - TABLE IX. INDEX 100) . FIGURES 41/ FOR SALE PRICES OF MONTANA LAND (1957-1959 1960 1962 1963 1964 1965 1966 Irrigated Land 108 114 119 122 126 134 Dry Farm Land 112 123 127 130 134 144 Grazing Land 121 131 135 143 151 164 TABLE X. ADJUSTED ANNUAL PERCENT CHANGE IN PRICE OF IRRIGATED LAND IN MONTANA. Year Index Factor Percent Level Change Percent ' 1966 134/134 100.0 1965 134/126 106.2 6.2 1964 134/122 109.5 3.3 1963 134/119 112.4 2.9 1962 134/114 116.2 3.8 1961 134/111 est. 120.5 4.3 1960 134/108 124.0 3.5 Average percent change per year = 4.0% 41/ Ibid., pp. 9-10 75 The factor used to adjust each individual sale is shown in the column headed by (TFR) in the tabulation report. 2 A comparison was made of the average of the r terms of the groups of sales in all areas by group. These results are shown in Table XI below. These results indicate that the group type with the largest amount of explained sale price variation was the group of livestock ranches. TABLE XI. AVERAGE r2 VALUES FOR SALES GROUPS BY CONSIDERING SEPARATE DISTRICT r2 VALUES. Group Type . 2 Ave. r Irrigated Farms .3692 Wheat Farms .2653 Livestock Ranches .5268 Multiple Regression Statistics The purposes for using multiple regression analysis are either to form a model that may be used to predict a sale price from market data or test certain variables for their importance in influencing market values. Many of the samples used in this study were smaller in size than desired for testing a number of variables. However, this is a realistic problem confronting appraisers. In many instances there isn't a large number of sales in one type of area to serve as comparables. In spite of the size limitation of the groups in this study a number of significant results appear. 2 A comparison might first be made for the range of the computed R 2 and the typical r range of the simple linear regression models. The TABLE XII. SUMMARY OF RESULTS OF THE LINEAR REGRESSION MODEL BY DISTRICTS WITH SALES UNADJUSTED FOR TIME. Constant District Group Type : No. !Obser. !Dependent: ! Variable: Indep. : Variable: Term "a" : "B" : : Coeff.: t :Sig. t : : 95 % : 2r Billings Irr. 32 Sale P/A PU/A 45.33 456.09 5.06 Yes .4613 Wht. 6 Sale P/A FU / A 47.10 127.30 .53 No .0664 Lvs tk. 23 Sale P/A A/AU 68.88 - .99 -6.37 Yes .6593 Butte Irr. 34 Sale P/A FU / A 119.52 448.32 2.87 Yes .2048 Wht. 17 Sale P/A FU / A 65.99 587.51 3.78 Yes .2015 Lvs tk. 22 Sale P/A A/AU 75.29 -.912 -3.95 Yes .4383 Glendive Irr. 15 Sale P/A FU/A 47.07 185.59 3.01 Yes .4119 Wht. 33 Sale P/A FU / A 18.04 846.01 3.94 Yes .3344 Lvs tk. 12 Sale P/A A/AU 47.07 -.533 -2.53 Yes .3913 Gt. Falls Irr. 13 Sale P/A FU/A 49.78 116.65 2.82 Yes .4210 Wht. 33 Sale P/A FU/A 21.83 424.41 3.94 Yes .3337 Lvs tk. 21 Sale P/A A/AU 74.69 -2.20 -5.60 Yes .6233 Missoula Irr. 13 Sale P/A FU/A 132.51 418.30 2.28 Yes .3225 Wht. 0 Sale P/A Lvs tk. 14 Sale P/A A/AU 86.51 — . 84 -3.47 Yes .5013 Combined Irr. 107 Sale P/A FU/A 131.81 211.41 3.03 Yes .0808 Wht. 89 Sale P/A FU/A 32.61 539.43 4.44 Yes .1848 Lvs tk. 92 Sale P/A A/AU 65.61 —. 844 -8.26 Yes .4316 TABLE XIII. SUMMARY OF RESULTS OF THE LINEAR REGRESSION MODEL BY DISTRICT WITH SALES ADJUSTED FOR TIME. District :Group : :Type : N !Dependent: !Variable : Indep. :Cons tant VariabIe!Term "a" : "B" :Coeff. t : Sig. t 95 % r2 Billings Irr. 32 Sale P/A FU / A 53.97 465.29 5.02 Yes .4566 Wht. 6 Sale P/A FU/A 64.53 82.89 .29 No .0210 Lvs tk. 23 Sale P/A A/AU 81.49 - 1.19 -6.47 Yes .6664 Butte Irr. 34 Sale P/A FU/A 141.54 542.71 2.92 Yes .2103 Wht. 17 Sale P/A FU/A 67.34 764.94 2.46 Yes .2874 Lvstk. 22 Sale P/A A/AU 85.23 - 1.01 -3.96 Yes .4398 Glendive Irr. 15 Sale P/A FU/A 50.19 229.59 3.02 Yes .4124 Wht. 33 Sale P/A FU/A 18.99 1068.40 4.75 Yes .4218 Lvs tk„ 12 Sale P/A A/AU 54.40 - .61 -2.63 Yes .4091 Gt. Falls Irr. 13 Sale P/A FU/A 53.12 143.01 3.22 Yes .4857 Wht. 33 Sale P/A FU/A 23.27 547.74 3.91 Yes .3309 Lvstk. 21 Sale P/A A/AU 96.99 - 2.99 -5.90 Yes .6471 Missoula Irr. 13 Sale P/A FU/A 164.36 453.25 2.07 Yes .2809 Wht. 0 Sale P/A Lvs tk. 14 Sale P/A A/AU 101.24 - .96 -3.27 Yes .4718 Combined Irr. 107 Sale P/A FU/A 157.92 221.95 2.72 Yes .0661 Wht. 89 Sale P/A FU/A 36.18 675.28 5.15 Yes .2340 Lvstk. 92 Sale P/A A/AU 77.07 -.997 -8.41 Yes .4402 78 - typical r ranged from 0.30 to 0.60. The use of added variables increased 2 the R values to a range of 0.54 to 0.86. While the productivity variable in the simple linear cases is accounting for a major amount of market variation, additional factors are also important. However, there still remains part of the market variation which is accounted for by other 2 variables than those used in this study. The average of the R terms by group type of sales indicates that the group type with the highest amount of explained variation in the sale price was the livestock ranch group. This can be seen from Table XIV below. TABLE XIV. AVERAGE R2 VALUES FOR SALE GROUPS BY CONSIDERING SEPARATE DISTRICT R2 VALUES. Group Type Ave. R2 Irrigated Farms .7423 Wheat Farms .6328 Livestock Ranches .7785 Some idea of the variables that occurred most often significant may be indicative of the variables that often influence market price. In some cases significance of the variable is limited by sample size but the variables that are most often significant, are reasonable. These results are summarized in the Table XV (page 79). Multiple regression was tried with the use of shift variables. 42/ The purpose of the shift variables in the multiple regression equation 42/ N. R. Draper and H . Smith, Applied Regression Analysis, John Wiley and Sons, Inc., New York, 1966, pp. 134-142. 79 is to account for specific area differences. The form of the multiple regression equation then becomes. Y' = aX + B1X1 + b9X0 + b„X„ + b.X. + b.X, + ... + b X 0 1 1 2 2 3 3 4 4 5 3 n n where the value of X^ through X^.is 0 or I. The value of X^ is always I. When,the term aX^ is used to represent a district such as the Billings District, then the adjustment for any other district is that district coefficient combined with the aX^ coefficient. These shift coefficients are. shown in Tables XVIII, XIX AND XX;(pages 83, 84 and 85). TABLE XV. RELATIVE FREQUENCY OF SIGNIFICANT VARIABLES FROM MULTIPLE REGRESSION ANALYSIS FOR ALL GROUPS OF SALES. Variable !Productivity : : : : : :Sever-: :A/AU or FU/A :Size:MI/Oil:MI/Twh:TimejAdd-On:Blde:ence : PCT L No. Times Significant 10 4 2 4 2 3 4 0 I No. Times• Tested 14 14 13 . 13 13 13 14 3 I Another look may be taken at the relative frequency of the signifi­ cant variables when the groups of sales were combined and multiple regres­ sion results computed with the use of the shift variables. See Table XVI (page 80). The results of the data in Tables XV above and Table XVI (page 80) indicate that sample size did influence the variables that tested significant. However, there is an indication that the variables productivity, buildings, and size are most,frequently significant. 80 - TABLE XVI. RELATIVE FREQUENCY OF SIGNIFICANT VARIABLES FROM MULTIPLE REGRESSION FOR COMBINED GROUPS OF SALES. !Productivity: : : : : :A/Au or FU/A:Size:Ml/0il:MI/Twn:Time:Add- : On .'Bldk : Sever-: :ence : PCT L No. Times Significant; 3 3 I 2 2 0 3 0 . 0 No. Times Tested 3 3 I 2 3 3 3 0 I A comparison might be made as to the use of combined groups with shift variables and individual data groups. The combined groups do 2 involve further averaging.. In general, the R values for the combined groups tended to be lower. However, the overall model was significant as measured by the F value for all.three combined groups and tended to be higher than for individual district groups. The time variable coefficient which was computed for the, combined groups was statistically significant for two of the three combined groups. This variable tested significant for irrigated farms and livestock ranches. It is interesting to compare the average percentage increase per year from the multiple regression results with that indicated by the U.S.D.A. statistics. The partial net regression coefficient for time in the combined irrigated farms group was 9.69. This figure is interpreted to mean that on the average for the sales studied, the sale price per acre increased $9.69 per year. The standard error in this coefficient is 5.16. However, if the 9.69 figure is used and divided by an ,average 81 - sale price of $207,40 per acre, the percent increase per year is 4.68 percento The percentage increase per year may be computed similarly for the range land sales. A time increment per year of $2.11 per acre was computed. Based on an average sale price per acre of the grazing land of $40.10, a figure of 5.25 percent is indicated as the percent increase per year for grazing land sales. As was noted previously in the section on time adjustments, the U.S.D.A. figures showed a 4.0 percent increase per year for irrigated land and a 5.8 percent increase per year for grazing land. There was only one group of livestock ranch sales that had a testable number of sales with some leased land. This group which was tested for the influence of leased land was the Butte Livestock Ranch group. The partial net regression coefficient for the percentage lease variable of these ranches was 47.21 with a standard error of 26.52. Since the amount of lease was read as a proportion; i.e., numerically .24, .35, etc., a ranch with .10 percent of the operation on leased land would - on the average sell for $4.72 per acre more . than one without the lease, not considering the standard error. Predicting Sales Price with Multiple Regression Coefficients To illustrate the type of variation that might be expected if multiple regression coefficients were used to forecast a sale price, the factors of the sales were used to compute a predicted sale-price. In other words, after the coefficients were computed from the sales data, an estimate of the sale price that would have been predicted on the average, considering 82 - these variables, was calculated. See Appendix.E . Two figures from these data pages are shown in Table XXI (page 86) for each of the sale groups. These two figures are the average absolute residual and the percentage that this residual is of the average actual price. A comparison of the residuals by groups indicates that the irrigated farms had a smaller average group residual in comparison to average actual price as is shown in Table XVII below. However, all three groups showed similar results. TABLE XVII. SUMMARY OF RESIDUALS BY TYPE OF SALES. Group Type Average Absolute Residual. Ave.' Group Res. Pet.,of Ave..Act. in Price Irrigated Farms 176.05 17.18 Wheat Farms 14.71 18.07 Livestock Ranches 7.25 20.40 Project Report Analysis It is usual for staff appraisers for the Montana Highway■Commission to submit a project report of sale data and market information for the particular area in which the parcels to be appraised are located. This report usually contains a detailed analysis of all comparable sales which . were investigated. The most comparable sales cited for any particular subject may only be a few of the total number for which a detailed analysis was made. In this manner the project report becomes a detailed study of the entire market for the particular area. One project report of irrigated and dry farm sales was submitted for analysis from the Glendive District. This report was one which had been TABLE XVIII. MULTIPLE LINEAR REGRESSION EQUATION COEFFICIENTS FOR IRRIGATED FARMS District : N i "a" : FU/A : Total Acres :MI/OIL:MI/TWN : Time : Add : : On : Bide: Sever- ence ; F * * * * * Billings 32 224.81 306.10 * -.363 -9.26 -4.88 * 3.59 -60.94 18.63 * — .8663 22.21 Butte 34 145.17 307.98 -.0954 5.66 -6.98 6.19 196.15 21.04 — .6180 6.01 Glendive 15 61.68 132.46 * -.130 6.94 -1.28 2.19 — ** 6.44 — .5650 1.73 Gt. Falls 13 101.48 118.67 * -.109 * 6.41 -7.35 0.0009 _** 1.14 1.97 .8608 4.41 Missoula 13 120.25 448.43 * -.627 * -40.19 6.31 * 1.20 * -30.74 22.61 * — .8016 2.88 Combined 107 157.28 24.21 -181.00 -217.36 34.14 287.01 Billings Butte Glendive G. Falls Missoula -.150 Shift Shift Shift Shift Shift 7.30 -5.62 9.63 8.33 15.02 .5804 11.94 * Statistically different from 0 at 90 percent or above. **Variable not statistically testible in District. TABLE XIX. MULTIPLE LINEAR REGRESSION EQUATION COEFFICIENTS FOR WHEAT FARMS. District : N i "a" : FU/A : Total Acres :MI/OIL:MI/TWN: Time : Add On : :Sever-: : : Bldgience : R^ : F * * Billings 6 -25.30 595.98 _** _** _** _** _** 7.91 * .7586 4.71 Butte 17 85.52 439.69 -.1382 3.79 — . 860 4.50 * 2.86 11.48 — .6414 2.30 Glendive 33 -12.97 1010.27 .0054 .677 -.260 4.86 4.76 -.259 .5847 5.02 * * * Gt. Falls 33 45.24 350.31 -.0060 1.32 -1.32 -1.05 -.748 5.77 -5.25 .5467 3.61 * * * * Combined 89 465.83 -.026 .9044 -.969 1.32 -3.43 8.94 .5732 10.47 -4.35 Billings Shift 77.74 Butte Shift 53.88 Glendive Shift 34.80 G. Falls Shift * Statistically different from 0 at 90 percent or above **Variable not statistically testible in District. TABLE XX. MULTIPLE LINEAR REGRESSION EQUATION COEFFICIENTS FOR LIVESTOCK RANCHES District : N . "a" . . A/AU zTotal =Acres : : : :MI/OIL:MI/TWN = Time : Add : : On :Bldg.: Sever-=Pct : „ : ence =Lease= R^ : -F Billings 23 31.95 * -.621 -.0010 * -.642 * .179 2.12 * 2.57 * 3.77 * — * * .7982 * 8.47 Butte 22 17.16 -.317 * -.00325 -1.37 .254 3.45 17.16 4.58 — 47.21 .8439 8.78 Glendive 12 29.93 -.685 * -.0036 -3.00 -.387 9.39 -1.34 .926 — — ** .6443 1.03 Gt. Falls 21 79.61 -1.87 -.00024 -.197 -.220 .393 -3.08 .044 1.095 — ** .7941 5.78 Missoula 14 45.40 -.480 * -.0145 * 5.78 * 1.37 7.53 * -22.10 -2.04 * — — ** .8120 3.70 * Combined 92 24.57 9.61 -.609 Billings Butte -.0015 -.565 .071 2.11 5.31 3.25 17.85 .7348 16.62 ))m * * .157 Glendive -1.39 G. Falls 27.40 Missoula * Statistically different from 0 at 90 percent or above. **Variable not statistically testible in District. TABLE XXI. SUMMARY OF MULTIPLE LINEAR REGRESSION MODEL BY DISTRICT. District :Group :Type No. Obser. : : No. :Dependent: Indep. !Variable !Variables No. Stat. : : Sig. Indep. : : Variables-90%: F Sig • F 95% R2 :Ave. Ab.:Ave. !Residual:Ave. !Predicted: Ab. Res. Act. S.P x 100 Billings Irr. 32 Sale P/A 7 5 22.21 Yes .8663 30.78 14.20 Wht. 6 Sale P/A 2 2 4.71 No .7586 5.65 9.77 Lvs tk. 23 Sale P/A 7 2 8.47 Yes .7982 6.11 24.36 Butte Irr. 34 Sale P/A 7 4 6.01 Yes .6180 73.73 28.21 Wht. 17 Sale P/A 7 I 2.30 No .6414 32.32 27.97 Lvs tk. 22 Sale P/A 8 6 8.78 Yes .8432 6.97 13.17 Glendive Irr. 15 Sale P/A 6 0 1.73 No .5650 19.80 16.69 Wht. 33 Sale P/A 7 2 5.01 Yes .5847 8.68 12.47 Lvs tk. 12 Sale P/A 7 I 1.03 No .6443 9.14 36.01 Gt. Falls Irr. 13 Sale P/A 7 I 4.41 No .8608 10.12 9.70 Wht. 33 Sale P/A 8 3 3.61 Yes .5467 12.20 22.08 Lvs tk. 21 Sale P/A 8 I 5.78 Yes .7941 4.77 13.63 Missoula Irr. 13 Sale P/A 7 2 2.88 No .8016 42.62 17.12 Wht. 0 Sale P/A Lvs tk. 14 Sale P/A 7 0 3.70 No .8120 9.23 14.25 Combined Irr. 107 Sale P/A 7/14* 5 10.83 Yes .5804 __ Wht. 89 Sale P/A 7/13* 4 9.40 Yes .5732 — — — — Lvs tk. 92 Sale P/A 7/14* 6 17.90 Yes .7311 — — * Includes Shift Variables Used 87 - used for a particular highway project in 1965. Both linear and multiple regression statistics were computed for this group of sales. These coefficients were used to forecast a sale price for a group of subject parcels with the results compared to the value the appraiser had originally assigned to the parcel. The results of the predicted values for the sales on this project, and the predicted values of the subjects are shown in the Glendive section of Appendix E . A tabulation report for these project sales and the appraisals of the parcels is shown in Appendix B . Since the group of appraisals was fairly representative of the group of sales, the trend lines for both the sales and appraisals are shown on the sale data graph. See Figure 14 (page 88). It is interesting to note the similarity of the trend lines with the appraisal trend line being slightly above the trend line for the sales although statistical error limits would allow the lines to cross. A comparison of the values predicted for the parcels and those arrived at through the use of regres­ sion analysis is shown in Table XXII (page 89). In only one instance the deviations between the predicted market value of the subject and that value estimated by the appraiser exceeded $20.00 per acre. The 2 multiple R value for the sales data as shown in Appendix D was .9554. 500 _ .SfiLES-RPPRS IIG94-3 (3) 7G Trend of SalesLJ Q/ 400 CJ CC _____ Trend of Appraisals + Sale Observation 0 Appraisal Observations FEED UNITS/RCRE Figure 14. Graph of Sales and Appraisals on Project I IG 94-3(9) 76. TABLE XXII. PARCEL PREDICTIONS BASED ON FARM SALES INFORMATION OF PROJECT IIG94-3(9)76 IN THE GLENDIVE DISTRICT. !Appraiser' Parcel:Est. SP/A No. : 1965 :SP/A Range : s !indicated by : :Most Comparable: ; Sales ! Appraisal: W.r.t. : Range : Predicted SP/A I Variable :Pred. :W.r.t. :Range : Predicted : SP/A : 6 Variables : !Deviations :Pred. :of 6 Variables :W.r.t.!Predicted SP/A !Range :W.r.t. Annr. I 54.68 44.87 - 62.50 In 49.65 In 35.76 Below 18.92 2 47.50 44.87 - 27.78 Above 39.42 In 58.55 Above 11.05 3 60.05 50.00 - 64.23 In 58.77 In 62.38 In 2.33 4 154.89 137.93 - 198.57 In 172.46 In 178.82 In 23.93 5 170.39 100.00 - 172.41 In 145.62 In 161.47 In -8.92 6 180.00 100.00 - 172.41 Above 158.15 In 175.62 Above -4.38 7 65.00 50.00 - 64.23 Above 58.18 In 79.13 Above 14.13 8 70.00 58.75 - 64.23 Above 58.95 In 63.66 In -6.34 10 62.50 50.00 - 64.23 In 50.35 In 76.43 Above 13.93 11 45.00 28.58 - 44.87 Above 32.88 In 42.42 In -2.58 oo VO CHAPTER VI EVALUATION OF RESULTS Productivity Variables, Feed Units per Acre and Acres per Animal Unit The productivity variables, feed units per acre and acres per animal unit which were calculated from land classifications provide a method for rating a property over all on a productivity basis. The productivity ratings of the land types which are made for county tax. purposes appear to be conservative. • A check with the field appraisers who were familiar with the sales indicates in general that the carrying capacities and production ratings of the lands are conservative. Low carrying capacity ratings will, of course, yield higher sale price per animal unit figures. The accuracy of the feed-units-per-^acre .variable and acres-per- animal-unit variable depend to a great extent on the conversion of crop and hay production into animal unit months of feed. Wheat production appears to be converted least accurately; however, this method does allow for the consideration of wheat and other crops as part of the typical production for a diversified farm or■ranch. For farms which are virtually all wheat or dry land grain, the feed unit per acre rating may be directly converted,into a bushel per acre rating. The use of a productivity calculation which approaches the actual or best estimate of the farm or ranch production is superior to an abstract, weighted average rating of the farm. The results of this study indicate that,this overall variable rating is a close approximation of - actual farm productivity and that this variable enables a correlation to 91 - be made between sale price and productivity in a manner which incorporates some of the same thinking that is present in the minds of.the buyers and sellers at the .time of the sale. Linear Regression Model There appears to be a number of interesting and useful inferences that may be drawn from the simple linear regression model. All of the sample groups of sales except one small sample of wheat farms tested statistically significant. The inference which may be drawn from this result appears to be . that the use of a composite productivity variable is a logical, valid approach in correlating a group of rural sales. The graphical method of displaying this correlation allows for other individual adjustments when comparing or selecting comparable sales. The use of the linear,regression model is further substantiated by the similarities and logical differences that appear for the trend lines of,similar type properties in different areas of the state. An application of how this type of trend analysis may be used in right-of-way acquisition problems or other fair market appraisals is > illustrated in the project report analyzed from the Glendive District. A comparison may be.made of the subject parcels and the market trend; For large groups of subjects which are similar in nature to the sale properties, a comparison of the trends of the sales and appraisals may be made as shown in Figure 14 (page 88). If only a few parcels were being appraised so that a trend analysis is not possible for thq, appraisals, individual appraisals may still be compared to the market 92 - trend. All subject parcels need not lie above the market trend line, as adjustments for buildings, location, and other factors may suggest a value that is below. This method does have some use in explaining an appraisal in relation to the market to a client. This type of analysis is illustrated in Figure 15 below. O Trend of Sales ^ Subject # I less than #4. Similar Ioca- Feed Units Per Acre Figure 15. Hypothetical Subject Appraisal Shown in Relation to the Most Comparable Market Sales. A similar type of analysis may be made by mortgage loan institu­ tions , The trends of sales, appraisals, and loans may be charted. In many cases it may be typical to have an appraised value for agricultural purposes which is less than the market value. Likewise the amount loaned is some proportion of this appraised value. A hypothetical analysis of this type is illustrated in Figure 16 (page 93). An inference is apparent concerning the dollars invested per feed unit or animal unit. Traditionally it has been said that "good land was under priced and poor land over priced". The data of this study indicate 93 - jTrend of Sales Trend of Appraisals •Trend of Loans Feed Units Per Acre Figure 16. Comparison of Hypothetical Market, Appraisal and Loan Trends. that there is a definite trend toward higher investments per feed unit or animal unit for the less productive properties. This may be illus­ trated from the data of this study by taking the combined, unadjusted trend lines for each of the three groups of sales. The resulting figures as the per animal unit prices or per feed unit prices are computed graphically and shown in Figures 17, 18, and 19 (pages 94 and 95). The important point of this inference is that sale price per animal unit of feed unit was not constant for a given general area but varied with the particular productive quality of the property. With reference to the number of dollars invested per unit, some generalizations may be inferred as to the profit and net returns per acre. If the operating cost per acre of irrigated farms is similar regardless of land quality, then a unit of feed is more profitably produced on a high quality land type of farm because less acres and hence less cost were used to produce it. 94 - 400 v > 350 300 0)o •H M .U 0) I— I cd CA) 225 200 100 0 .5 1.0 Feed Units Per Acre Figure 17. Investment Per Feed Unit of Irrigated Farms at Two Levels of Productivity. $825/AU Combined Sales Trend for Livestock Ranches $1250/AU A/AU Figure 18. Investment Per Animal Unit of Livestock Ranches at Two Levels of Productivity. 95 - Combined Sales Trend for Wheat Farms "$800/FU $1100/FU Figure 19. Investment Per Feed Unit of Wheat Farms at Two Levels of Productivity. A few comments should be made about the general use of linear rela­ tionships. In this study linear relationships were hypothesized to exist. However, it is almost certain that non-linear relationships may exist. An example of a non-linear relationship is that of livestock ranches. A curvilinear or hyperbolic curve is anticipated as illustrated in Figure 4 (page 21). A portion of this curve may be approximated by a linear line as was done in this study. The type of ranches studied were those in the mid range where this type of approximation could be used, (see Figure 20, page 96). As a final comment on the results of the linear regression model, it is clear that there are price variations in different parts of the state for a given productive class of land. This result is apparent 96 - Linear Approximation of Mid Range Sales 60 -- 40 -- 20 - - Expected Sales Distribution Figure 20. Mid Range Approximation of Non-Linear Sales Distribution. from the trend lines which have been summarized in Figures 11, 12, and 13 (pages 71, 72, and 73). Multiple Regression Model The multiple regression model demonstrates the use of the statis­ tical method of computing coefficients from a group of sales to be used in the prediction of the market value of other properties. In this study the coefficients were used to compute a predicted value for the sales. It was observed that the deviations of the predicted price were o reduced when the value of the R term increased. A project report group was also analyzed and the sale price was estimated for a group of subject properties. The results of this attempt were shown in Table XXII (page 89). Also, the multiple regression model demonstrates how significant variables may be isolated or recognized in a group of sales. - 97 - The chief limiting factor in the multiple regression method of analysis for this study was the size of sample. The significance of the overall model or of individual variables was reduced. The effect of sample size may be observed by comparing the combined groups. The level of the F 2 value came up and the R went down when the combined groups were compared to individual groups. This would indicate that statistical significance of the model was increased but that the combined groups introduced more 2 variation and hence a lower R value. This study does point up a very important fact that the particular significant variables in one area may not be the most significant ones in another area or for another type of property. Time It would appear from this study that time should be a factor that is given more consideration in market value appraisals. When time factors were considered separately for each sale, the result was a uniform adjust­ ment upward of the trend lines. Time tested significant at the 90 per­ cent level.or above in only two of the 14 groups of sales but it did test significant in two of the three combined groups of sales. An 4 adjustment for timfe by some index is often controversial. The argument against time adjustment of sales is that this adjustment can be made with other adjustments overall without citing a particular index or group of successive sales which may be questioned. The argument for using some time index in market value appraisals is that at least the dollar inflation is taken into account before other adjustments are made between 98 - the most comparable sales and the subjects. The choice of whether to use United States Department of Agriculture statistics or United States Department of Commerce statistics is one of preference. Of course, any wide area statistics will overrate a static area and underrate a rapidly developing region. The fact remains that in this study the trend lines of the sales data were all shifted upward would seem to indicate that the best indication of current market trends might be made by using the time adjustment. Summary It would appear from the results of this study that an overall productivity variable can be developed with statistically significant, and logical results. The hypothesis that such a variable could be developed and used is accepted. The first hypothesis to be tested for the multiple regression model was that a statistically significant model could be obtained as measured by the F value. One-half of the sample groups of sales studied tested significant at the 95 percent level. Statistical significance appears to be limited by sample size. The sale groups with 20 observations,or more tested significant. Those groups with less than 20 observations were the groups that did not test significant. It, therefore, appears possible to develop a significant model provided that sample .size is large enough. The hypothesis that significant variables may be delineated and ranked for importance is also a function of sample size. In some cases 99 it may be necessary to work out more exact relationships to adequately test and rank the variables. It can be shown that the .variables which are significant change from area to area. It is inconclusive as to whether multiple regression can be 2 developed as a rural property model which will yield such values of R as .95 consistently, or which could forecast a sale price to be within 10 percent of the true price, 95 percent of the time. The key appears to lie in having larger groups of local sales where the relationships between variables are studied in greater detail. CHAPTER VII SUGGESTIONS FOR FURTHER STUDY It would appear that the multiple regression model could be improved and successfully used to predict market values. In some instances the relationship of sale price per acre to the particular variables used might be better expressed as some curvilinear function rather than as a linear function. A second suggestion is the expansion of sample size. A multiple regression study undertaken by any appraisal organization could be improved by keeping records of sales throughout the area. In this way larger local groups of sales could be analyzed. This would allow for better tests of significance. Other variables not used in the models of this study should be considered. One such additional variable which could be considered is one which would account for the terms of purchase. This is a complex variable made up of many factors which change from year to year and may need to be broken down into components. A study of the interrelationships between variables could be under­ taken. For example, it has been shown in this study and others that both buildings and time affect sale prices. However, it might also be useful to know if buildings are changing in importance with time. In other words, is the market giving more or less recognition to buildings as a trend. This type of problem is approached through the use of inter­ action variables. Interaction variables may be generated as illustrated in the following multiple regression equation: 1 0 1 - where is the time variable, building rating variable and X ^ is the interaction variable formed by .taking the product of X^ and X^. A study such as was undertaken might be more meaningful if the capitalization rates were computed. To obtain the income figures would require a very extensive research program in itself. In many cases the income figures of a sale are not kept separate from other parts of the farming operation. An improvement in the definition or determination of productivity variables and factors may be possible. The factors which convert crop production may need to be tempered to arrive at a better contribution of this type of acreage to the whole. The simple linear regression model.could readily be carried on in the everyday type of field assignments of appraisers of rural property. For appraisers in Montana the county reclassification records of lands might be tempered for appraisal purposes to more nearly reflect typical current average production or carrying capacity figures. In many instances a correlation of this type could be performed with use of a scatter diagram graph without.the computation of the statistics. APPENDICES APPENDIX A STATISTICAL FORMULA SUMMARY FOR THE LINEAR REGRESSION MODEL Equation for the Linear Trend Line Y = A + B X E Y = Y' = Y E Est. (A-I) Conditions of Least Squares and Equations to Compute A and B 43/ The constants A and B are computed such that the sum (S^) of the squared deviations, n „ iI ' - V (A-2) about the trend line will be minimized and the sum (S') of the deviations, = I Mb y B b J t L i=l b I i (A-3) will equal zero for a sufficiently large sample. Partial derivatives are used to derive the normal equations to solve for the constants A and B . L = S = % (A + B X - Y 1 i=l 1 )' (A-4) I ■ 2 J1'4 + 6 X1 • (A-5) 43/ For a discussion on the derivation of normal equations see Howard W. Alexander, Elements of Mathematical Statistics, John Wiley & Sons, Inc., New York, 1961, pp. 288-290. 104 - as = 2 V (A + B X - Y j X = 0 SB 1=1 1 1 i By determinants; N ZX ZX ZX2 A ZY ZX ZXY ZX2 D B N ZY ZX ZXY (A-6) (A-7) (A-8) (A-9) Basic Statistical Formulas 44/ Total Sum of Squares (Total SS) v ~ 2 i=l 1 (A-IO) Regression Sum of Squares (Regression SS) n - o I (Y' - Y) 1=1 (A-Il) Residual Sum of Squares (Residual SS) I (Y. - Y')2 1=1 (A-12) Coefficient of Determination ^2 _ Regression SS Total SS (A-13) Coefficient of Correlation H Il i-i M (A-14) Variance c2 = Total SS Y n - I (A-15) 44/ Of the many good statistical references on this subject, three have been used to develop the program formulas for the linear regression analysis phase of this study. Ezekiel and Fox, op, cit., p . 19; Li, op. cit., pp. 292-321; Steele and Torie, op. cit. , pp. 17-171. 105 - Standard Deviation S = S2 (A-16) y y Residual Mean Square Q2 = Residual SS (A-l7) y x n - 2 Standard Error of Estimate S = S2 (A-18) y -x y -x X Sum of Squares (SSX) 2 SSX = X2 -!HL- = Zx2 (A-19) n Standard Error of b s f - S 2 X ( A - 2 0 ) S S X T Ratio S b - Sb2 ( A - 2 1 ) t = b-B0 where B = 0 (A-22) Sb F Value y - Regression SS ''A-07' Residual Mean Square APPENDIX B TABULATION REPORTS SHOWING SALES ADJUSTED AND UNADJUSTED FOR TIME 107 TABLE XXIII. HEADINGS USED IN THE TABULATION REPORTS. A/AU ACRT ASP ASP/A ASP/AU ASP/EU ASR ASV AUH AUMT AUR AUT BLDV BV/A EU FU/A INC INCR LANDV LV/FU SALE P TFR NO. Acres per animal unit Total deeded acres in farm or ranch Adjusted sale price (if adjusted for time) Adjusted sale price per acre Adjusted sale price per animal unit Adjusted sale price per feed unit Ratio of assessed value to sale price Assessed value Year long animal units of hay Total animal unit months of feed Animal units of range for the specified grazing period (* following the number indicates special grazing period) Total year long.animal units Building contribution value Building contribution value per acre Total year long feed units (AUMT/12) Feed units per acre (total feed units/total acres) Annual income, gross or net Ratio of annual income to sale price Land value (total adjusted sale price less building contribution value) Land value per feed unit . Sale price Time factor (e.g., a 4 percent adjustment upward would be entered as,I.04) Number assigned to sale in each group APPRAISAL DATA FOR R. J. REHER* BOZEMAN, MONT IRR• FARMS - BILLINGS DIST NAME/NO. YR SALE P ASV TFR ASP BLOV LANDV ACRT LV/A BV/A ASP/A ASR FU FU/A ASP/FU LV/FU INC INCR I 65 28070. 6750. 1.00 28070. 5000. 23070. 157.0 146. 31. 178. .24 51. .329 542 445 0. 0.0002 66 17500. 38 50. 1.00 17500. 5000. 12500. 51.0 245. 98. 343. .22 27. .531 645 460 Q 0*0003 65 22200. 3300. 1.00 22200. 2500. 19700. 90.0 218. 27. 246. .14 42. .476 517 459 0. 0*0004 64 16650. 5200. 1.00 16650. 600. 16050. 167.0 96. 3. 99. .31 55. .334 297 286 o. O 0005 64 8200. 650. 1.00 8200. 0. 8200. 61.0 134. 0. 134. .07 14. .245 547 547 o. 0*0006 64 5070. 670. 1.00 5070. 0. 5070. 41.0 123. 0. 123. .13 10. .262 470 470 o. 0*0007 64 16000. 1950. 1.00 16000. 1000. 15000. 80.0 187. 12. 200. .12 22. .276 723 678 O *0008 66 13800. 1900. 1.00 13800. 200. 13600. 82.0 165. 2. 168. .13 26. .322 522 514 o. 0*0009 65 12800. 2150. 1.00 12800. 0. 12800. 80.0 160. 0. 160. .16 25. .314 508 508 o. O 00010 65 8000. 930. 1.00 8000. 0. 8000. 80.0 100. 0. 100. .11 16. .208 479 479 o.11 63 18050. 4300. 1.00 18050. 1050. 17000. 200.0 85. 5. 90. .23 40. .203 442 417 0.12 65 18000. 4000. 1.00 18000. 6000. 12000. 123.0 97. 48. 146. .22 27. .220 664 442 o. 0*000 13 63 34500. 6750. 1.00 34500. 5000. 29500. 202.0 146. 24. 170. .19 63. .313 545 466 o Jooo14 65 8000. 1950. 1.00 8000. 0. 8000. 80.0 100. 0. 100. .24 31. .389 256 256 0. 0* QQQ15 66 36000. 4000. 1.00 36000. 12000. 24000. 278.0 86. 43. 129. .11 29. .107 1208 805 o.16 65 12800. 3100. 1.00 12800. 0. 12800. 40.0 320. 0. 320. .24 22. .562 568 568 0.17 65 10250. 1500. 1.00 10250. 0. 10250. 35.0 292. 0. 292. .14 21. .625 468 46818 65 16900. 5750. 1.00 16900. 4700. 12200. 50.0 244. 94. 338. .34 21. .432 781 564 o. o J ooo19 66 21000. 2440. 1.00 21000. 3000. 18000. 80.0 225. 37. 262. .11 32. .406 646 553 0. 0*00020 66 16200. 1410. 1.00 16200. 0. 16200. 64.0 253. 0. 253. .08 29. .458 552 552 0* OOO21 64 14750. 850. 1.00 14750. 500. 14250. 55.0 259. 9. 268. .05 16. .301 890 860 Q*22 64 18000. 2700. 1.00 18000. 5000. 13000. 40.0 325. 125. 450. .15 18. .458 981 70923 62 32000. 5400. 1.00 32000. 900. 31100. 195.0 159. 4. 164. .16 119. .611 268 26024 64 6125. 1084. 1.00 6125. 0. 6125. 22.0 278. 0. 278. .17 16. .770 361 361 o. 0*00026 62 12000. 2200. 1.00 12000. 0. 12000. 109.0 H O . 0. H O . .18 24. .227 483 483 0. o Jooo27 65 10500. 1250. 1.00 10500. 0. 10500. 40.0 262. 0. 262. .11 20. .515 509 509 0. 0* OOO28 65 14500. 2250. 1.00 14500. 4000. 10500. 40.0 262. 100. 362. .15 21. .546 662 480 o. O O OO29 65 35530. 5700. 1.00 35530. 2000. 33530. 73.0 459. 27. 486. .16 37. .515 944 891 o. O OOO30 65 42200. 6050. 1.00 42200. 4000. 38200. 223.0 171. 17. 189. .14 81. .366 516 467 0. 0*00031 65 24300. 2000. 1.00 24300. 3500. 20800. 80.0 260. 43. 303. .08 32. .411 738 631 0. oJooo 32 60 20600. 3700. 1.00 20600. 2320. 18280. 165.0 H O . 14. 124. .17 32. .198 628 557 0*00033 60 56400. 10600. 1.00 56400. 15900. 40500. 722.0 56. 22. 78. .18 60. .083 938 673 0. 0.000 TOTAL NO. OF FARMS = 32 AVERAGE ASP/FU = 603. AVERAGE LVZFU = 526. AVERAGE ASSESSMENT-SALE RATIO = .16 NO INCOME VALUES GIVEN STATISTICAL ANALYSIS Y VAR = ASPZA X VAR = FUZA REGRESSION EQUATION Y = 45.31 + 456.11 X RSQ = .4613 SY = 106.71 YAVE = 216.76 SB = 89.97 R = .6792 SYX = 79.61 XAVE = .375 T = 5.06 SOURCE DF SS MS F DUE TO REG I •16287471E+06 .16287471E+06 25.69 ABOUT REG 30 .19015114E+06 ,63383713E+04 TOTAL 31 .35302660E+06 108 APPRAISAL DATA FOR R • J . REMER» BOZEMAN, MONT. - IRR • FARMS - BILLINGS DIST • NAME/NO. YR SALE P ASV TFR ASP BLDV LANDV ACRT LV/A BV/A ASP/A ASR FU FU/A ASP/FU LV/FU INC INCR I 65 28070. 6750. 1.04 29192. 5000. 24192. 157.0 154. 31. 185. .24 51. .329 564 467 0. 0.0002 66 17500. 3850. 1.00 17500. 5000. 12500. 51.0 245. 98. 343. .22 27. .531 645 460 0.3 65 22200. 3300. 1.04 23088. 2500. 20588. 90.0 228. 27. 256. .14 42. .476 537 479 o. O *0004 64 16650. 5200. 1.08 17982. 600. 17382. 167.0 104. 3. 107. .31 55. .334 321 310 0. o* ooo5 64 8200. 650. 1.08 8856. 0. 8856. 61.0 145. 0. 145. .07 14. .245 591 591 0. O OOO6 64 5070 • 670. 1.08 5475. 0. 5475. 41.0 133. 0. 133. . 13 10. .262 507 507 0. O OOO7 64 16000. 1950. 1.08 17280. 1000. 16280. 80.0 203. 12. 216. .12 22. .276 781 735 o.8 66 13800. 1900. 1.00 13800. 200. 13600. 82.0 165. 2. 168. .13 26. .322 522 514 0.9 65 12800. 2150. 1.04 13312. 0. 13312. 80.0 166. 0. 166. .16 25. .314 529 529 o. O OOO10 65 8000 . 930. 1.04 8320. 0. 8320. 80.0 104. 0. 104. .11 16. .208 498 498 o. o’ooo 11 63 18050. 4300. 1.12 20216. 1050. 19166. 200.0 95. 5. 101. .23 40. .203 496 470 O *00012 65 18000. 4000. 1.04 18720. 6000. 12720. 123.0 103. 48. 152. .22 27. .220 690 469 Q* 13 63 34500. 6750. 1.12 38640. 5000. 33640. 202.0 166. 24. 191. .19 63. .313 610 531 0.000 0.000 14 65 8000 . 1950. 1.04 8320. 0. 8320. 80.0 104. 0. 104. .24 31. .389 267 267 o.15 66 36000. 4000. 1.00 36000. 12000. 24000. 278.0 86. 43. 129. .11 29. . 107 1208 805 o. 16 65 12800. 3100. 1.04 13312. 0. 13312. 40.0 332. 0. 332. .24 22. .562 591 591 o. 0*00017 65 10250. 1500. 1.04 10660. 0. 10660. 35.0 304. 0. 304. .14 21. .625 487 487 o. 0.00018 65 16900 . 5750. 1.04 17576. 4700. 12876. 50.0 257. 94. 351. .34 21. .432 813 595 0.19 66 21000. 2440. 1.00 21000. 3000. 18000. 80.0 225. 37. 262. .11 32. .406 646 553 0.00020 66 16200. 1410. 1.00 16200. 0. 16200. 64.0 253. 0. 253. .08 29. .458 552 552 0.21 64 14750. 850. 1.08 15930. 500. 15430. 55.0 280. 9. 289. .05 16. .301 961 931 o. o Jooo22 64 18000. 2700. 1.08 19440. 5000. 14440. 40.0 361. 125. 486. .15 18. .458 1060 787 0* 000 23 62 32000. 5400. 1.16 37120. 900. 36220. 195.0 185. 4. 190. .16 119. .611 311 303 0. 0.00024 64 6125. 1084. 1.08 6615 . 0. 6615. 22.0 300. 0. 300. .17 16. .770 390 390 o.26 62 12000. 2200. 1.16 13920. 0. 13920. 109.0 127. 0. 127. .18 24. .227 560 56027 65 10500. 1250. 1.04 10920. 0. 10920. 40.0 273. 0. 273. .11 20. .515 529 529 0* 0.00028 65 14500. 2250. 1.04 15080. 4000. 11080. 40.0 277. 100. 377. .15 21. .546 689 506 o * 29 65 35530. 5700. 1.04 36951. 2000. 34951. 73.0 478. 27. 506. .16 37. .515 982 928 0* 0*00030 65 42200. 6050. 1.04 43888. 4000. 39888. 223.0 178. 17. 196. .14 81. .366 537 488 Q ’ 0.000 0.000 0.000 0.000 31 65 24300. 2000. 1.04 25272. 3500. 21772. 80.0 272. 43. 315. .08 32. .411 767 661 0* 32 60 20600. 3700. 1.24 25544. 2320. 23224. 165.0 140. 14. 154. .17 32. . 198 779 708 0 ’33 TOTAL NO. OF 60 FARMS 56400. 32 10600. 1.24 69936. 15900. 54036. 722.0 74. 22. 96. .18 60. .083 1163 899 0. AVERAGE ASP/FU = 643. AVERAGE LV/FU = 566. AVERAGE ASSESSMENT-SALE RATIO = .16 NO INCOME VALUES GIVEN STATISTICAL ANALYSIS Y VAR = ASP/A X VAR = FU/A REGRESSION EQUATION Y = 53.97 + 465.29 X RSO = .4566 SY = 109.41 YAVE » 228.88 SB = 92.65 R = .6757 SYX = 81.98 XAVE = .375 T = 5.02 SOURCE DF SS MS F DUE TO REG I .16949852E+06 .16 49852E+06 25.21 ABOUT REG 30 •20164330E+06 .67214433E+04 TOTAL 31 .37114269E+06 109 APPRAISAL DATA FOR R. J . REMER» BOZEMAN, MONT. - WHEAT FARMS - BILLINGS DIST NAME/NO. YR SALE P ASV TFR ASP BLDV LANDV ACRT LV/A BV/A ASP/A ASR FU FU/A ASP/FU LV/FU INC INCR I 61 37500. 11286. 1.00 37500. 11420. 26080. 880.0 29. 12. 42. .30 34. .038 1094 761 0. 0.000Z 63 26500. 8210. 1.00 26500. 9160. 17340. 320.0 54. 28. 82. .30 37. .118 700 458 0.3 62 16000. 4855. 1.00 16000. 0. 16000. 320.0 50. 0. 50. .30 33. .106 471 471 o. 0*0004 60 16000. 6238. 1.00 16000. 0. 16000. 320.0 50. 0. 50. • 38 33. .106 471 471 o. 0* OOO5 61 37000. 9378. 1.00 37000. 500. 36500. 761.0 47. 0. 48. .25 65. .085 568 561 0.000 0.000 TOTAL NO. UF 60 FARMS 35000. I = 6 6804. 1.00 35000. 11480. 23520. 480.0 49. 23. — 72. .19 24. .050 1443 970 ol AVERAGE ASP/FU = 791. AVERAGE LV/FU = 615. AVERAGE ASSESSMENT-SALE RATIO = .29 NO INCOME VALUES GIVEN ----------------------- STATISTICAL ANALYSIS I I 47.10 + 127.30 X RSO = .0664 SY S 16.06 YAVE = 5 7 . 8 2 SB = 238.53 R = .2578 SYX = 17.35 XAVE = .084 T = .53 SOURCE OF SS DUE IO REG I .85802807E+0Z ABOUT REG 4 .12049049E+04 HS 85802807E+02 30122622E+03 F .28 H O APPRAISAL DATA FOR R. J. REMER» BOZEMAN, MONT. - WHEAT FARMS - BILLINGS *D 1ST, NAME/NO. YR SALE P ASV TFR ASP BLDV LANDV ACRT LV/A BV/A ASP/A ASR FU FU/A ASP/FU LV/FU INC INCR I 61 37500. 11286. 1.25 46875. 11420. 35455. 880.0 40. 12. 53. .30 34. .038 1368 1034 o. n nnn2 63 26500. 8210. 1.15 30475. 9160. 21315. 320.0 66. 28. 95. .30 37. .118 806 563 0. n* nnn3 62 16000. 4855. 1.20 19200. 0. 19200. 320.0 60. 0. 60. .30 33. .106 565 565 0. n nnp4 60 16000. 6238. 1.30 20800. 0. 20800. 320.0 65. 0. 65. .38 33. .106 612 612 0.000 0.000 0.000 5 61 37000. 9378. 1.25 46250. 500. 45750. 761.0 60. 0. 60. .25 65. .085 710 703 CU6 60 35000. 6804. 1.30 45500. 11480. 34020. 480.0 70. 23. 94. .19 24. .050 1876 1403 0. TOTAL NO. OF FARMS = 6 AVERAGE ASP/FU = 990. AVERAGE LV/FU - 813. AVERAGE ASSESSMENT-SALE RATIO = .29 NO INCOME VALUES GIVEN STATISTICAL ANALYSIS Y VAR = ASP/A X VAR = FU/A — REGRESSION EQUATION Y = 64.53 + 82.89 X RSQ » .0210 R = .1451 SY SYX - 18.58 YAVE = = 20.56 XAVE = 71.51 SB = 282 .i . 084 T = ., SOURCE DUE TO REG ABOUT REG TOTAL DF I 4 5 SS MS F .36382421E+02 .36382421E+02 .08 .16913988E+04 .42284970E+03 •17277812E+04 * ill APPRAISAL DATA FOR R. J. REMER,_BOZEHAN, MONT. - LVSTK RANCHES - B I L U N G S OIST. NAME/NO. YR SALE P ASV TFR ASP _ BLOV LANDV ACRJ LV/A BV/A ASP/A ASR AUR AUH AUT A/AU ASP/AU INC I 64 192000. 27966. 1.00 192000. 8000. 184000. 8981.0 20.48 0. 21.37 .14 183 28 182 49.3 1054 0. 60 71000. 13722. 1.00 71000. 14730. 56270. 1881.0 29.91 7. 37.74 .19 36 65 95 19.6 740 0 . 3 62 200000. 19404. 1.00 200000. 17855. 182145. 2329.0 78.20 7 . 85.87 .09 55 129 176 13.2 1135 0 . 4 63 43600. 7272. 1.00 43600. 2000. 41600. 1480.0 28.10 I. 29.45 .16 39 26 58 25.2 742 0 .5 65 8000. 1202. 1.00 8000. 0. 8000. 320.0 25.00 0 . 25.00 .15 9 O 8 39.6 9906 65 45000. 8343. 1.00 45000. 3785. 41215. 699.0 58.96 5. 64.37 .18 9 41 49 14.1 910 Q 7 64 105000. 12173. 1.00 105000. 15000. 90000. 2073.0 43.41 7. 50.65 .11 37 71 102 20.2 1025 8 64 1600. 746. 1.00 1600. 0. 1600. 296.0 5.40 0. 5.40 .46 6 O 5 55.2 298 0 .9 64 3200. 746. 1.00 3200. 0. 3200. 296.0 10.81 0. 10.81 .23 6 O 5 55.2 596 0 . 10 64 3200. 403. 1.00 3200. 0. 3200. 160.0 20.00 0. 20.00 .12 3 O 2 55.2 1104 0 . 11 65 2000. 635. 1.00 2000. 0. 2000. 160.0 12.50 0. 12.50 .31 5* O 4 36.8 460 0 . 12 63 11500. 2410. 1.00 11500. 0. 11500. 956.0 12.02 0. 1 2 . 0 2 .20 23* O 17 55.2 664 0 . 13 63 20000. 6164. 1.00 20000. 2 0 0 0 . 18000. 1640.0 10.97 I. 12.19 .30 39* O 29 666 0. 62 3200. 764. 1.00 3200. 0. 3200. 320.0 10.00 0. 10.00 .23 6 O 5 58. I 581 15 64 37460. 5496. 1.00 37460. 0. 37460. 1873.0 20.00 0. 20.00 39 O 32 57.1 1143 0 .16 63 60000. 9368. 1.00 60000. 2000. 58000. 3080.0 18.83 0. 19.48 .15 53* 16 56 54.1 1055 0 .17 64 1600. 403. 1.00 1600. 0. 1600. 160.0 10.00 0. 10.00 • 25 3 O 2 55.2 55?TB 60 45000. 1 1 0 7 5 . 1.00 45000. 1500. 43500. 3505.0 12.41 0. 12.83 .24 75 29 93 37.6 483 0.19 64 11000. 1158. 1.00 11000. 0. 11000. 530.0 20.75 0. 20.75 . 1 0 10 O 8 63.3 1315 0 . “ZD 65 4000. 5 9 5 . 1.00 4000. 0. 4000. 160.0 25.00 0. 25.00 . 14 4 O 4 39.6 21 64 11200. 1456. 1.00 11200. 0. 11200. 5 5 9 . 0 20.03 0 . 20.03 .13 12 O 10 53.6 1075 22 65 25000. 4002. 1.00 25000. 2500. 22500. 936.0 24.03 2. 26.70 .16 22 O 18 50.9 1360 0 . 23 65 32000. 3723. 1.00 32000. 0. 32000. 1275.0 25.09 0 . 25.09 — «11 ... 3* __O 26 48.8 1224 0. TOTAL NO. OF RANCHES = 23 AVERAGE ASPZAU = 877. GENERAL GRAZING PD. = 10.0 MO. ♦SPECIAL GRAZING PO. •i»__ ----------------- STATISTICAL ANALYSIS "Y"VAR " ASPTAT--)T VAR *-"F07A Hira^ 5T01TT5lJSTIWr~Y“---68.86 + -- --^5f “ITSir* " .6MT T? - 18.95 YAVE = 25.10 SB = .15 R = —.8119__SYX «___ 11.32__XAVE = 44.016__ T__= -6.37 SOURCE OF SS____________HS_________ F "TxJE-To REG---- T .52T32T33M-4 - T52132l33E+04---- 40.63 ABOUT REG 21 .26938910E+04 .12828052E+03 TOTAL 22 .79071151E+04 +  + + + +  + + + +  + + + +  + + + 0.000 0.000 0.000 0.000 0.000 0.000 +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + INCR 112 APPRAISAL DATA FOR R • J. REMER , BOZEMAN , MONT. - LVSTK RANCHES - I3 ILLINGS D 1ST. NAME/NO. YR SALE P ASV TFR ASP BLDV LANDV ACRT LV/A BV/A ASP/A ASR AUR AUH AUT A/AU ASP/AU heEs hEsi I 64 192000. 27966. 1.12 215040. 8000. 207040. 8981.0 23.05 0. 23.94 • 14 183 29 182 49.3 1181 0. 0.0002 60 71000. 13722. 1.36 96560. 14730. 81830. 1881.0 43.50 7. 51.33 .19 36 65 95 19.6 1006 0. 0.0003 62 200000. 19404. 1.24 248000. 17855. 230145. 2329.0 98.81 7. 106.48 .09 55 129 176 13.2 1407 0. 0.0004 63 43600. 7272. 1.18 51448. 2000. 49448. 1480.0 33.41 I. 34.76 .16 39 26 58 25.2 876 O• O.OOO5 65 8 000. 1202. 1.06 8480. 0. 8480. 320.0 26.50 0. 26.50 .15 9 O 8 39.6 1049 O. 0.0006 65 45000. 8343. 1.06 47700. 3785. 43915. 699.0 62.82 5. 68.24 .18 9 41 49 14. I 965 0. 0.0007 64 105000. 12173. 1.12 117600. 15000. 102600. 2073.0 49.49 7. 56.72 .11 37 71 102 20.2 1148 0. 0.0008 64 1600 . 746. 1.12 1792. 0. 1792. 296.0 6.05 0. 6.05 .46 6 O 5 55.2 334 0. 0.0009 64 3200. 746. 1.12 3584. 0. 3584. 296.0 12. 10 0. 12. 10 .23 6 O 5 55.2 668 0. 0.00010 64 3200. 403. 1.12 3584. 0. 3584. 160.0 22.40 0. 22.40 .12 3 O 2 55.2 1236 0. 0.00011 65 2000. 635. 1.06 2120. 0. 2120. 160.0 13.25 0. 13.25 .31 5* O 4 36.8 487 0. 0.000 0. 0.000 12 63 11500. 2410. 1.18 13570. 0. 13570. 956.0 14. 19 0. 14.19 .20 23* O 17 55.2 783 13 63 20000. 6164. 1.18 23600. 2000. 21600. 1640.0 13.17 I. 14.39 .30 39* O 29 54.6 786 0. 0.00014 62 3200. 764. 1.24 3968. 0. 3968. 320.0 12.40 0. 12.40 .23 6 O 5 58. I 720 0. 0.000 0. 0.000 15 64 37460. 5496. 1.12 41955. 0. 41955. 1873.0 22.40 0. 22.40 .14 39 O 32 57.1 1231 16 63 60000. 9368. 1.18 70800. 2000. 68800. 3080.0 22.33 0. 22.98 .15 53* 16 56 54. I 1245 0. 0.00017 64 1600. 403. I. 12 1792. 0. 1792. 160.0 11.20 0. 11.20 .25 3 O 2 55.2 0. 0.000 0. 0.000 18 60 45000. 11075. 1.36 61200. 1500. 59700. 3505.0 17.03 0. 17.46 .24 75 29 93 37.6 65719 64 11000. 1158. 1.12 12320. 0. 12320. 530.0 23.24 0. 23.24 . 10 10 O 8 63.3 1473 0. 0.00020 65 4000. 59 5. 1.06 4240. 0. 4240. 160.0 26.50 0. 26.50 . 14 4 O 4 39.6 1049 0. 0.000 0. 0.000 0. 0.000 21 64 11200. 1456. 1.12 12544. 0. 12544. 559.0 22.44 0. 22.44 . 13 12 O 10 53.6 1204 22 65 25000. 4002. 1.06 26500. 2500. 24000. 936.0 25.64 2. 28.31 .16 22 O 18 50.9 144223 TOTAL NO. OF 65 32000. RANCHES = 3723. 23 1.06 33920. 0. 33920. 1275.0 26.60 0. 26.60 .11 31 O 26 48.8 1298 0. 0.000 AVERAGE ASP/AU = 996. GENERAL GRAZING PD. = 10.0 MO. =StSPEC I AL GRAZING PD. AVERAGE ASSESSMENT-SALE RATIO = .19 NO INCOME VALUES GIVEN STATISTICAL ANALYSIS Y VAR = ASP/A X VAR = FU/A REGRESSION EQUATION Y = 81.49 + -1.19 X RSO = .6664 SY = 22.66 YAVE = 28.86 SB = .18 R = -.8163 SYX = 13.40 XAVE = 44.016 T = -6.47 SOURCE DF SS MS F DUE TO REG I •75349435E+04 75349435E+04 41.96 ABOUT REG 21 • 37708981E+04 I7956657E+03 TOTAL 22 •11305843E+05 113 APPRAISAL DATA FOR R. J. R EM ER» BOZEMAN, MONT. - IRR• FARMS - BUTTE DIST. NAME/NO. YR SALE P ASV TFR ASP BLDV LANDV ACRT LV/A BV/A ASP/A ASR FU FU/A ASP/FU LV/FU INC INCR I 61 40000. 12140. 1.00 40000. 5500. 34500. 140.0 246. 39. 285. .30 49. .352 810 699 0. 0.0002 58 40000. 13665. 1.00 40000. 6800. 33200. 232.0 143. 29. 172. .34 78. .336 511 424 0. 0.0003 62 75000. 12280. 1.00 75000. 5000. 70000. 313.0 223. 15. 239. .16 119. .381 628 586 0.4 62 26000. 2100. 1.00 26000. 840. 25160. 168.0 149. 5. 154. • 08 23. .140 1098 1062 0. 0*0005 61 80000. 23845. 1.00 80000. 5000. 75000. 758.0 98. 6. 105. .29 231. .305 345 323 o. 0.0006 61 30000. 4835. 1.00 30000. 9000. 21000. 210.0 100. 42. 142. • 16 51. .243 586 410 0. 7 61 15000. 1220. 1.00 15000. 1500. 13500. 158.0 85. 9. 94. • 08 5. .032 2885 2596 o. 0.0008 62 50000. 11505. 1.00 50000. 6550. 43450. 158.0 275. 41. 316. • 23 75. .480 658 572 0.9 61 77000. 13610. 1.00 77000. 5000. 72000. 342.0 210. 14. 225. .17 135. .394 570 533 0.000 0.000 0.000 0.000 0.000 0.000 10 62 88500. 13910. 1.00 88500. 30000. 58500. 117.0 500. 256. 756. .15 55. .476 1587 1049 u m 11 61 28000. 5265. 1.00 28000. 5000. 23000. 160.0 143. 31. 175. • 18 44. .279 626 514 Q12 59 83500. 16145. 1.00 83500. 5500. 78000. 388.0 201. 14. 215. .19 100. .258 833 778 13 60 48000. 6560. 1.00 48000. 632. 47368. 158.0 299. 4. 303. • 13 82. .524 579 57114 58 16000. 1590. 1.00 16000. 3400. 12600. 72.0 175. 47. 222. .09 10. .145 1527 1202 0.15 62 35000. 5265. 1.00 35000. 5000. 30000. 162.0 185. 30. 216. .15 44. .275 783 671 o.16 58 28500. 5380. 1.00 28500. 5000. 23500. 226.0 103. 22. 126. • 18 49. .220 573 472 o. 0.000 0.000 17 61 79000. 15085. 1.00 79000. 15000. 64000. 160.0 400. 93. 493. .19 27. .170 2904 235218 62 42000. 3340. 1.00 42000. 0. 42000. 93.0 451. 0. 451. .07 56. .611 738 738 0.19 60 8000. 0. 1.00 8000. 0. 8000. 75.0 106. 0. 106. 0.00 20. .273 389 389 0.20 59 78000. 0. 1.00 78000. 0. 78000. 235.0 331. 0. 331. 0.00 89. .382 868 868 0. 0.00021 62 35000. 4755. 1.00 35000. 0. 35000. 154.0 227. 0. 227. .13 13. .088 2561 2561 0.22 62 19000. 16720. 1.00 19000. 0. 19000. 60.0 316. 0. 316. • 88 27. .460 687 687 0.000 0.000 0.000 0.000 0.000 23 62 35000. 5795. 1.00 35000. 0. 35000. 175.0 200. 0. 200. .16 84. .483 413 413 0*24 62 71500. 16735. 1.00 71500. 500. 71000. 264.0 268. I. 270. • 23 133. .504 536 53225 61 100000. 14830. 1.00 100000. 500. 99500. 314.0 316. I. 318. .14 126. .401 792 78826 62 9000. 1900. 1.00 9000. 0. 9000. 96.0 93. 0. 93. .21 32. .336 278 278 0.27 57 100000. 0. 1.00 100000. 0. 100000. 250.0 400. 0. 400. 0.00 127. .508 786 786 0.28 61 200000. 16140. 1.00 200000. 0. 200000. 390.0 512. 0. 512. • 08 100. .257 1993 1993 o.29 60 50000. 7910. 1.00 50000. 10000. 40000. 287.0 139. 34. 174. .15 22. .078 2213 1770 0. 0.00030 58 65000. 12890. 1.00 65000. 1350. 63650. 197.0 323. 6. 329. .19 73. .375 879 860 o. 31 62 60000. 30705. 1.00 60000. 4000. 56000. 480.0 116. 8. 125. .51 99. .206 603 563 o. o!ooo32 64 65000. 8585. 1.00 65000. 5000. 60000. 200.0 300. 25. 325. .13 64. .320 1014 936 0. 0.00033 65 116000. 14925. 1.00 116000. 10090. 105910. 510.0 207. 19. 227. • 12 97. .192 1184 1081 o.34 TOTAL NO. OF 65 324000. FARMS = 34 44840. 1.00 324000. 17700. 306300. 1428.0 214. 12. 226. .13 358. .251 903 854 0. 0.000 AVERAGE ASP/FU = 1010. AVERAGE LV/FU = 909. AVERAGE ASSESSMENT-SALE RATIO = .20 NO INCOME VALUES GIVEN STATISTICAL ANALYSIS Y VAR = A S P / A X VAR = FU/A REGRESSION EQUATION Y = 119.52 + 448.32 X RSQ = .2048 SY = 140.05 YAVE = 261.30 SB = 156.13 R = .4526 SYX = 126.82 XAVE = .316 T = 2.87 SOURCE OF SS MS F DUE TO REG I •13261942E+06 .13261942E+06 8.24 ABOUT REG 32 .51470294E+06 .16084466E+05 TOTAL 33 .64732253E+06 114 APPRAISAL. DATA FOR R• J. REMER i BOZEMAN, MONT. - IRR • FARMS - BUTTE D 1ST • NAME/NO. YR SALE P ASV TFR ASP BLDV LANDV ACRT LV/A BV/A ASP/A ASR FU FU/A ASP/FU LV/FU INC INCR I 61 40000. 12140. 1.20 48000. 5500. 42500. 140.0 303. 39. 342. .30 49. .352 972 861 0. 0.000 2 58 40000. 13665. 1.32 52800. 6800. 46000. 232.0 198. 29. 227. .34 78. .336 675 588 0. 0.000 3 62 75000. 12280. 1.16 87000. 5000. 82000. 313.0 261. 15. 277. .16 119. .381 728 687 0. 0.000 4 62 26000. 2100. 1.16 30160. 840. 29320. 168.0 174. 5. 179. .08 23. . 140 1273 1238 0. 0.000 5 61 80000. 23845. 1.20 96000. 5000. 91000. 758.0 120. 6. 126. .29 231. .305 414 393 0. 0.000 6 61 30000. 4835. 1.20 36000. 9000. 27000. 210.0 128. 42. 171. .16 51. .243 703 527 0. 0.000 7 61 15000. 1220. 1.20 18000. 1500. 16500. 158.0 104. 9. 113. .08 5. .032 3462 3173 0. 0.000 8 62 50000. 11505. 1.16 58000. 6550. 51450. 158.0 325. 41. 367. .23 75. .480 763 677 0. 0.000 9 61 77000 . 13610. 1.20 92400. 5000. 87400. 342.0 255. 14. 270. .17 135. .394 684 647 0. 0.000 10 62 88500. 13910. 1.16 102660. 30000. 72660. 117.0 621. 256. 877. .15 55. .476 1841 1303 0. 0.000 11 61 28000. 5265. 1.20 33600. 5000. 28600. 160.0 178. 31. 210. .18 44. .279 751 639 0. 0.00012 59 83500. 16145. 1.28 106880. 5500. 101380. 388.0 261. 14. 275. .19 100. .258 1066 1011 0. 0.000 13 60 48000. 6560. 1.24 59520. 632. 58888. 158.0 372. 4. 376. .13 82. .524 718 710 0. 0.00014 58 16000. 1590. 1.32 21120. 3400. 17720. 72.0 246. 47. 293. .09 10. . 145 2015 1691 0. 0.00015 62 35000. 5265. 1.16 40600. 5000. 35600. 162.0 219. 30. 250. .15 44. .275 908 796 0. 0.000 16 58 28500. 5380. 1.32 37620. 5000. 32620. 226.0 144. 22. 166. .18 49. .220 756 655 0. 0.00017 61 79000. 15085. 1.20 94800. 15000. 79800. 160.0 498. 93. 592. .19 27. .170 3484 2933 0. 0.00018 62 42000. 3340. 1.16 48720. 0. 48720. 93.0 523. 0. 523. .07 56. .611 856 856 0. 0.00019 60 8000. 0. 1.24 9920. 0. 9920. 75.0 132. 0. 132. 0.00 20. .273 482 482 0. 0.00020 59 78000. 0. 1.28 99840. 0. 99840. 235.0 424. 0. 424. 0.00 89. .382 1111 1111 0. 0.00021 62 35000. 4755. 1.16 40600. 0. 40600. 154.0 263. 0. 263. .13 13. .088 2971 2971 0. 0.00022 62 19000. 16720. 1.16 22040. 0. 22040. 60.0 367. 0. 367. .88 27. .460 797 797 0. 0.00023 62 35000. 5795. 1.16 40600. 0. 40600. 175.0 232. 0. 232. .16 84. .483 479 479 0• O•OOO24 62 71500. 16735. 1.16 82940. 500. 82440. 264.0 312. I. 314. .23 133. .504 622 618 0. 0.000 25 61 100000. 14830. 1.20 120000. 500. 119500. 314.0 380. I. 382. .14 126. .401 950 946 0. 0.00026 62 9000. 1900. 1.16 10440. 0. 10440. 96.0 108. 0. 108. .21 32. .336 322 322 0. 0.00027 57 100000. 0. 1.36 136000. 0. 136000. 250.0 544. 0. 544. 0.00 127. .508 1069 1069 0. 0.00028 61 200000. 16140. 1.20 240000. 0. 240000. 390.0 615. 0. 615. .08 100. .257 2392 2392 0. 0.00029 60 50000. 7910. 1.24 62000. 10000. 52000. 287.0 181. 34. 216. .15 22. .078 2744 2301 0. 0.00030 58 65000. 12890. 1.32 85800. 1350. 84450. 197.0 428. 6. 435. .19 73. .375 1160 1142 0. 0.000 31 62 60000. 30705. 1.16 69600. 4000. 65600. 480.0 136. 8. 145. .51 99. .206 700 660 0. 0.00032 64 65000. 8585. 1.08 70200. 5000. 65200. 200.0 326. 25. 351. .13 64. .320 1095 1017 0. 0.00033 65 116000. 14925. 1.04 120640. 10090. 110550. 510.0 216. 19. 236. .12 97. .192 1231 1128 0. 0.00034 65 324000. 44840. 1.04 336960. 17700. 319260. 1428.0 223. 12. 235. .13 358. .251 939 890 0. 0.000 TOTAL NO. OF FARMS = 34 AVERAGE ASP/FU = 1210. AVERAGE LV/FU = 1109. AVERAGE ASSESSMENT-SALE RATIO = .20 NO INCOME VALUES GIVEN STATISTICAL ANALYSIS Y VAR = ASP/A X VAR = FU/A REGRESSION EQUATION Y = 141.54 + 542.71 X RSQ = .2103 SY * 167.30 YAVE = 313.18 SB = 185.85 R = .4586 SYX = 150.96 XAVE = .316 T = 2.92 SOURCE DF SS MS F DUE TO REG I .19434277E+06 I9434277E+06 8.52 ABOUT REG 32 •72934112E+06 22791910E+05 TOTAL 33 •92368407E+06 115 APPRAISAL DATA FOR R. J . REMER BOZEMAN, MONT. - WHEAT FARMS - BUTTE DIST. NAME/NO. YR SALE P ASV TFR ASP BLDV LANDV ACRT LV/A BV/A ASP/A ASR FU FU/A ASP/FU LV/FU INC I 61 26500. 4950. 1.00 26500. 0. 26500. 160.0 165. 0. 165. .18 43. .270 611 611 0. 2 63 48000. 8775. 1.00 48000. 0. 48000. 400.0 120. 0. 120. .18 38. .097 1231 123 I 0. 3 61 32450. 11445. 1.00 32450. 0. 32450. 268.0 121. 0. 121. .35 26. .098 1233 1233 0.4 59 20000. 0. 1.00 20000. 0. 20000. 158.0 126. 0. 126. 0.00 15. .096 1308 1308 o. 5 65 25600. 0. 1.00 25600. 0. 25600. 640.0 40. 0. 40. 0.00 20. .031 1253 1253 o.6 63 45000. 5305. 1.00 45000. 2675. 42325. 472.0 89. 5. 95. .11 29. .062 1517 1427 0.7 65 17000. 1780. 1.00 17000. 1050. 15950. 160.0 99. 6. 106. .10 8. .055 1907 1789 o. 8 62 19500. 0. 1.00 19500. 0. 19500. 338.0 57. 0. 57. 0.00 17. .053 1086 1086 o. 9 65 30500. 0. 1.00 30500. 9870. 20630. 314.0 65. 31. 97. 0.00 25. .080 1209 817 o. 10 64 18000. 0. 1.00 18000. 5000. 13000. 153.0 84. 32. 117. 0.00 11. .075 1550 1119 o. 11 61 21000. 0. 1.00 21000. 2500. 18500. 1022.0 18. 2. 20. 0.00 31. .031 660 581 0.12 62 25500. 0. 1.00 25500. 0. 25500. 670.0 38. 0. 38. 0.00 33. .049 765 765 0. 13 63 23500. 0. 1.00 23500. 7355. 16145. 158.0 102. 46. 148. 0.00 10. .063 2345 1611 14 65 4500. 0. 1.00 4500. 0. 4500. 154.0 29. 0. 29. 0.00 4. • 030 969 969 o.15 61 80000. 0. 1.00 80000. 11675. 68325. 666.0 102. 17. 120. 0.00 117. .175 683 583 o. 16 66 30300. 4845. 1.00 30300. 10000. 20300. 118.0 172. 84. 256. .15 8. .070 3622 2426 17 64 38000. 7585. 1.00 38000. 6000. 32000. 118.0 271. 50. 322. .19 14. .120 2667 2246 0. TOTAL NO. OF FARMS = 17 AVERAGE ASP/FU = 1448. AVERAGE LV/FU = 1238. AVERAGE ASSESSMENT-SALE RATIO = .18 NO INCOME VALUES GIVEN STATISTICAL ANALYSIS Y VAR = ASP/A X VAR = FU/A REGRESSION EQUATION* Y = 65.99 + 587.81 X RSQ = .2015 SY = 78.55 YAVE = 116.63 SB = 302.10 R = .4489 SYX = 72.49 XAVE = .086 T = 1.94 SOURCE DF SS MS F DUE TO REG I .19898927E+05 .19898927E+05 3.78 ABOUT REG 15 *78840788E+05 .52560525E+04 TOTAL 16 •98739701E+05 0.000 0.000 0.000 0.000 +  + + + +  + + + +  + + + 0.000 +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + INCR 116 APPRAISAL. DATA FOR R. J. REMER » BOZEMAN, MONT. - WHEAT FARMS - BUTTE! DIST. NAME/NO. YR SALE P ASV TFR ASP BLDV LANDV ACRT LV/A BV/A ASP/A ASR FU FU/A ASP/FU LV/FU INC I 61 26500. 4950. 1.25 33125. 0. 33125. 160.0 207. 0. 207. .18 43. .270 764 7642 63 48000. 8775. 1.15 55200. 0. 55200. 400.0 138. 0. 138. .18 38. .097 1416 1416 g"3 61 32450. 11445. 1.25 40562. 0. 40562. 268.0 151. 0. 151. .35 26. .098 1542 1542 Q*4 59 20000. 0. 1.35 27000. 0. 27000. 158.0 170. 0. 170. 0.00 15. .096 1765 1765 Q*5 65 25600. 0. 1.05 26880. 0. 26880. 640.0 42. 0. 42. 0.00 20. .031 1315 13156 63 45000. 5305. 1.15 51750. 2675. 49075. 472.0 103. 5. 109. .11 29. .062 1745 1655 Q*7 65 17000. 1780. 1.05 17850. 1050. 16800. 160.0 105. 6. 111. .10 8. .055 2002 1884 Q "8 62 19500. 0. 1.20 23400. 0. 23400. 338.0 69. 0. 69. 0.00 17. .053 1304 1304 Q*9 65 30500. 0. 1.05 32025. 9870. 22155. 314.0 70. 31. 101. 0.00 25. .080 1269 87810 64 18000. 0. 1.10 19800. 5000. 14800. 153.0 96. 32. 129. 0.00 11. .075 1705 127411 61 21000. 0. 1.25 26250. 2500. 23750. 1022.0 23. 2. 25. 0.00 31. .031 825 74612 62 25500. 0. 1.20 30600. 0. 30600. 670.0 45. 0. 45. 0.00 33. .049 918 918 Q*13 63 23500. 0. 1.15 27025. 7355. 19670. 158.0 124. 46. 171. 0.00 10. .063 2696 1962 Q "14 65 4500. 0. 1.05 4725. 0. 4725. 154.0 30. 0. 30. 0.00 4. .030 "15 61 80000. 0. 1.25 100000. 11675. 88325. 666 . O 132. 17. 150. 0.00 117. .175 854 \s4 O16 66 30300. 4845. 1.00 30300. 10000. 20300. 118.0 172. 84. 256. .15 8. .070 3622 2426 Q*I 7 TOTAL NO. OF 64 FARMS 38000. 17 7585. 1.10 41800. 6000. 35800. 118.0 303. 50. 354. .19 14. .120 2934 2513 0. AVERAGE ASP/FU = 1629. AVERAGE LV/FU = 1420. AVERAGE ASSESSMENT-SALE RATIO = .18 NO INCOME VALUES GIVEN STATISTICAL ANALYSIS Y VAR = ASP/A X VAR = FU/A REGRESSION EQUATION Y = 67.34 + 764.94 X RSO = .2874 SY = 85.59 YAVE = 133.25 SB = 310.94 R = .5361 SYX » 74.62 XAVE = .086 I = 2.46 SOURCE DF SS MS F DUE TO REG I .33698425E+05 .33698425E+05 6.05 ABOUT REG 15 •83526105E+05 .55684070E+04 TOTAL 16 .11722453E+06 0.000 0.000 0.000 0.000 +  + + + +  + + + +  + + + 0.000 +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + INCR APPRAISAL DATA FOR R. J. REMER« BOZEMAN, MONT. - LVSTK RANCHES - BUTTE DIST. NAME/NO. YR SALE P ASV TFR ASP BLDV LANDV ACRT LVZA BVZA ASPZA ASR AUR AUH AUT AZAU ASPZAU INC INCR I 64 67000. 0. 1.00 67000. 0. 67000. 2250.0 29.77 0. 29.77 0.00 111# O 51 44.0 1310 0. O OOO 2 61 19200. 0. 1.00 19200. 0. 19200. 640.0 30.00 0. 30.00 0.00 32* O 15 42.5 1277 0. 0*000 3 61 100000. 0. 1.00 100000. 12500. 87500. 1290.0 67.82 9. 77.51 0.00 33* 95 H O 11.6 901 0. O 000 6 63 30500. 0. 1.00 30500. 3500. 27000. 754.0 35.80 4. 40.45 0.00 26 55 74 10.1 411 o. O OOO 8 61 20000. 0. 1.00 20000. 0. 20000. 1796.0 11.13 0. 11.13 0.00 54* 12 46 38.7 431 0. 0*00010 64 165000. 0. 1.00 165000. 22000. 143000. 2800.0 51.07 7. 58.92 0.00 39* 324 349 8.0 472 0. 11 60 20000. 0. 1.00 20000. 0. 20000. 640.0 31.25 0. 31.25 0.00 28* O 17 36.0 1125 o. 12 65 14000. 0. 1.00 14000. 0. 14000. 632.0 22.15 0. 22.15 0.00 20* O 11 53.9 1195 o. 13 65 16500. 0. 1.00 16500. 0. 16500. 373.0 44.23 0. 44.23 0.00 8* O 5 72.0 3184 o. 16 63 85000. 0. 1.00 85000. 5000. 80000. 1481.0 54.01 3. 57.39 0.00 30 171 193 7.6 439 o. 17 67 117000. 0. 1.00 117000. 15000. 102000. 1160.0 87.93 12. 100.86 0.00 31* 117 134 8.6 872 o. 18 64 171600. 0. 1.00 171600. 6777. 164823. 1761.0 93.59 3. 97.44 0.00 76* 140 181 9.6 944 0. 19 61 160000. 0. 1.00 160000. 20100. 139900. 2500.0 55.96 8. 64.00 0.00 46* 60 91 27.4 1757 0. 20 63 150000. 0. 1.00 150000. 30590. 119410. 2219.0 53.81 13. 67.59 0.00 85* 67 124 17.8 1206 0. 21 64 110000. 0. 1.00 110000. 3640. 106360. 4293.0 24.77 0. 25.62 0.00 199* O 133 32.2 825 o. Q QQQ 22 65 250000. 0. 1.00 250000. 16420. 233580. 3282.0 71.17 5. 76.17 0.00 68 186 235 13.9 1062 o. o!ooo23 64 110000. 0. 1.00 110000. 10000. 100000. 1800.0 55.55 5. 61.11 0.00 33 155 178 10.0 615 o. O OOO24 64 100000. 0. 1.00 100000. 19600. 80400. 1080.0 74.44 18. 92.59 0.00 12 175 183 5.8 544 o. 0*00029 65 96 OOOO. 0. 1.00 960000. 46000. 914000. 23098.0 39.57 I. 41.56 0.00 873* 1093 1566 14.7 612 0. O OOO30 64 75000. 0. 1.00 75000. 7000. 68000. 2140.0 31.77 3. 35.04 0.00 46* 21 50 42.6 1493 o. 0*000 31 65 25000. 0. 1.00 25000. 0. 25000. 576.0 43.40 0. 43.40 0.00 14* 21 30 18.9 824 0. 32 64 75000. 0. 1.00 75000. 10000. 65000. 1322.0 49.16 7. 56.73 0.00 44* 84 111 11.8 670 0. 0.000 TOTAL NO. OF RANCHES = 22 I AVERAGE ASP/AU = 1008. GENERAL GRAZING PD. = 8.5 MO. ♦SPECIAL GRAZING PD. NO ASSESSMENT VALUES GIVEN NO INCOME VALUES GIVEN STATISTICAL ANALYSIS Y VAR = ASP/A X VAR = FU/A REGRESSION EQUATION Y = 75.29 + -.91 X RSQ = .4383 SY * 25.08 YAVE * 52.95 SB = R = -.6620 SYX = 19.26 XAVE = 24.487 T = -3.' SOURCE DF SS MS F DUE TO REG I •57925027E+04 .57 25027E+04 15.60 ABOUT REG 20 .74221682E+04 .37110841E+03 TOTAL 21 .13214672E+05 118 APPRAISAL DATA FOR R• J. REMER , BOZEMAN , MONT. - LVSTK RANCHES - IBUTTE I31ST. NAME/NO. YR SALE P ASV TFR ASP BLDV LANDV ACRT LV/A BV/A ASP/A ASR AUR AUH AUT A/AU ASP/AU INC INCR I 64 6 7000 . 0. 1.12 75040. 0. 75040. 2250.0 33.35 0. 33.35 0.00 111* O 51 44.0 1467 0. 0.0002 61 19200. 0. 1.30 24960. 0. 24960. 640.0 39.00 0. 39.00 0.00 32* O 15 42.5 1660 0. 0.0003 61 100000. 0. 1.30 130000. 12500. 117500. 1290.0 91.08 9. 100.77 0.00 33* 95 n o 11.6 1171 0. 0.0006 63 30500. 0. 1.18 35990. 3500. 32490. 754.0 43.09 4. 47.73 0.00 26 55 74 10. I 435 0. 0.0008 61 20000. 0. 1.30 26000. 0. 26000. 1796.0 14.47 0. 14.47 0.00 54* 12 46 38.7 561 0. 0.00010 64 165000. 0. 1.12 184800. 22000. 162800. 2800.0 58.14 7. 56.00 0.00 39* 324 349 8.0 528 0. 0.00011 60 20000. 0. 1.36 27200. 0. 27200. 640.0 42.50 0. 42.50 0.00 28* O 17 36.0 1530 0. 0.00012 65 14000. O. 1.06 14840. 0. 14840. 632.0 23.48 0. 23.48 0.00 20* O 11 53.9 1266 0. 0.00013 65 16500. O • 1.06 17490. 0. 17490. 373.0 46.89 0. 46.89 0.00 8* O 5 72.0 3376 0. 0.00016 63 85000. 0. 1.18 100300. 5000. 95300. 1481.0 64.34 3. 67.72 0.00 30 171 193 7.6 519 0. 0.00017 67 117000. 0. 1.00 117000. 15000. 102000. 1160.0 87.93 12. 100.86 0.00 31* 117 134 8.6 872 0. 0.00018 64 171600. 0. 1.12 192192. 6777. 185415. 1761.0 105.28 3. 109.13 0.00 76* 140 181 9.6 1057 0. 0.00019 61 160000. 0. 1.30 208000. 20100. 187900. 2500.0 75.16 8. 83.20 0.00 46* 60 91 27.4 2284 0. 0.00020 63 150000. 0. 1.18 177000. 30590. 146410. 2219.0 65.98 13. 79.76 0.00 85* 67 124 17.8 1424 O- o.non21 64 110000. 0. 1.12 123200. 3640. 119560. 4293.0 27.84 0. 28.69 0.00 199* O 133 32.2 924 V . VeWVV 0. 0.00022 65 250000. 0. 1.06 265000. 16420. 248580. 3282.0 75.74 5. 30.74 0.00 68 186 235 13.9 1126 0. 0.00023 64 110000 . 0. 1.12 123200. 10000. 113200. 1800.0 62.88 5. 68.44 0.00 33 155 178 10.0 688 0. 0.00024 64 100000. 0. 1.12 112000. 19600. 92400. 1080.0 85.55 18. 103.70 0.00 12 175 183 5.8 609 0. 0.00029 65 960000. 0. 1.06 1017600. 46000. 971600. 23098.0 42.06 I. 44.05 0.00 873* 1093 1566 14.7 649 0. 0.00030 64 75000. 0. 1.12 84000. 7000. 77000. 2140.0 35.98 3. 39.25 0.00 46* 21 50 42.6 1472 O• 0.00031 65 25000. 0. 1.06 26500. 0. 26500. 576.0 46.00 0. 46.00 0.00 14* 21 30 18.9 873 0. 0.00032 64 75000. 0. 1.12 84000. 10000. 74000. 1322.0 55.97 7. 63.54 0.00 44* 84 111 11.8 750 0. 0.000 TOTAL NO. OF RANCHES = 22 AVERAGE ASP/AU = 1159. GENERAL GRAZING PD. = 8.5 MO. -SPECIAL GRAZING PD. NO ASSESSMENT VALUES GIVEN NO INCOME VALUES GIVEN STATISTICAL ANALYSIS Y VAR = ASP/A X VAR = FU/A REGRESSION EQUATION Y = 85.23 + -1.01 X KSO = .4398 SY = 27.80 YAVE = 60.42 SB = .25 R = -.6631 SYX = 21.32 XAVE = 24.487 T = -3.96 SOURCE DF SS MS F DUE TO REG I .71417063E+04 .71417063E+04 15.70 ABOUT REG 20 .90960365E+04 .45480182E+03 TOTAL 21 .16237740E+05 119 APPRAISAL DATA FOR R. J. REMER• BOZEMAN, MONT. - IRR• FARMS - GLENDIVE DIST. NAME/NO. YR SALE P ASV TFR ASP BLDV LANDV ACRT LV/A BV/A ASP/A ASR FU FU/A ASP/FU LV/FU INC INCR I 63 30000. 0. 1.00 30000. 9000. 21000. 266.0 78. 33. 112. 0.00 132. .497 226 158 0. n nnn 2 63 6500. 0. 1.00 6500. 1500. 5000. 90.0 55. 16. 72. 0.00 24. .275 262 201 0. 3 63 5500. 0. 1.00 5500. 1500. 4000. 30.0 133. 50. 183. 0.00 7. .250 733 533 0. 0.000 5 60 30000. 0. 1.00 30000. 10200. 19800. 187.0 105. 54. 160. 0.00 102. .548 292 193 0. 6 62 28000. 0. 1.00 28000. 8300. 19700. 187.0 105. 44. 149. 0.00 102. .548 273 192 o. 7 62 16500. 0. 1.00 16500. 0. 165 00. 151.0 109. 0. 109. 0.00 53. .354 308 308 0. 0.000 8 61 16000. 0. 1.00 16000. 0. 16000. 118.0 135. 0. 135. 0.00 66 » .562 241 241 0. 0.0009 62 17000. 0. 1.00 17000. 2000. 15000. 242.0 61. 8. 70. 0.00 54. .224 313 276 0. 0.000 10 60 2000. 0. 1.00 2000. 0. 2000. 40.0 50. 0. 50. 0.00 9. .226 220 220 o. 11 59 23637. 0. 1.00 23637. 8000. 15637. 152.0 102. 52. 155. 0.00 67. .441 352 233 0. O OOQ 12 63 26000. 0. 1.00 26000. 0. 26000. 307.0 84. 0. 84. 0.00 96. .314 269 269 0.13 64 36000. 0. 1.00 36000. 2900. 33100. 700.0 47. 4. 51. 0.00 99. .141 362 333 0. 0.00014 62 20000. 0. 1.00 20000. 5390. 14610. 147.0 99. 36. 136. 0.00 39. .268 505 369 0.15 65 -8000. 0. 1.00 8000. 0. 8000. 60.0 133. 0. 133. 0.00 34. .581 229 229 o. O DQQ16 60 7000. 0. 1.00 7000. 0. 7000. 40.0 175. 0. 175. 0.00 21. .549 318 318 0. 0.000 TOTAL NO. OF FARMS = 15 AVERAGE ASP/FU = 327. AVERAGE LV/FU = 271. NO ASSESSMENT VALUES GIVEN NO INCOME VALUES GIVEN STATISTICAL ANALYSIS Y VAR = ASP/A X VAR = FU/A REGRESSION EQUATION Y * 47.07 + 185.57 X RSQ = .4118 SY - 44.11 YAVE = 118.64 SB = 61.50 R = .6417 SYX - 35.10 XAVE = .385 T = 3.01 SOURCE DF SS MS F DUE TO REG I .11219026E+05 .11219026E+05 9.10 ABOUT REG 13 .16021247E+05 •12324036E+04 TOTAL 14 •27240233E+05 120 APPRAISAL DATA FOR R . J. REMER * BOZEMAN, MONT. - IR R . FAlMS - GLENDIVE DIST. NAME/NO. YR SALE P ASV TFR ASP BLDV LANDV ACRT LV/A 8V/A ASP/A ASR FU FU/A ASP/FU LV/FU INC I 63 30000. 0. 1.12 33600. 9000. 24600. 266.0 92. 33. 126. 0.00 132. .497 253 185 o. 2 63 6 500. 0. 1.12 7280. 1500. 5780. 90.0 64. 16. 80. 0.00 24. .275 293 233 0.3 63 5500. 0. 1.12 6160. 1500. 4660. 30.0 155. 50. 205. 0.00 7. .250 821 621 0. 5 60 30000. 0. 1.24 37200. 10200. 27000. 187.0 144. 54. 198. 0.00 102. .548 362 263 6 62 28000. 0. 1.16 32480. 8300. 24180. 187.0 129. 44. 173. 0.00 102. .548 316 235 o.7 62 16500. 0. 1.16 19140. 0. 19140. 151.0 126. 0. 126. 0.00 53. .354 357 357 0. 8 61 16000. 0. 1.20 19200. 0. 19200. 118.0 162. 0. 162. 0.00 66 • .562 289 289 o.9 62 17000. 0. 1.16 19720. 2000. 17720. 242.0 73. 8. 81. 0.00 54. .224 363 326 0.10 60 2000. 0. 1.24 2480. 0. 2480. 40.0 62. 0. 62. 0.00 9. .226 273 273 o. 11 59 23637. 0. 1.28 30255. 8000. 22255. 152.0 146. 52. 199. 0.00 67. .441 450 331 0.12 63 26000. 0. 1.12 29120. 0. 29120. 307.0 94. 0. 94. 0.00 96. .314 301 30113 64 36000. 0. 1.08 38880. 2900. 35980. 700.0 51. 4. 55. 0.00 99. . 141 391 362 0*14 62 20000. 0. 1.16 23200. 5390. 17810. 147.0 121. 36. 157. 0.00 39. .268 586 450 0 *15 65 8000 . 0. 1.04 8320. 0. 8320. 60.0 138. 0. 138. 0.00 34. .581 238 238 Q16 60 7000. 0. 1.24 8680. 0. 8680. 40.0 217. 0. 217. 0.00 21. .549 394 394 o l TOTAL NO. OF FARMS = 15 AVERAGE ASP/FU = 379. AVERAGE LV/FU = 324. NO ASSESSMENT VALUES GIVEN NO INCOME VALUES GIVEN STATISTICAL ANALYSIS Y VAR = ASP/A X VAR = FU/A REGRESSION EQUATION Y = 50.19 + 229.59 X RSO = .4124 R = .6421 SY = SYX = 54.53 YAVE = 43.38 XAVE = 138.73 .385 SB = T = 76.00 3.02 SOURCE DF SS MS F DUE TO REG I .17172652E+05 .17172652E + 05 9.12 ABOUT REG 13 .24466405E+05 .18820311E+04 TOTAL 14 •41639020E+05 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 INCR 121 APPRAISAL DATA FOR R. J. REMER* BOZEMAN, MONT. - WHEAT FARMS - GLENDIVE 01ST. NAME/NO. YR SALE P ASV TFR ASP BLDV LANDV ACR C LV/A BV/A ASP/A ASR FU FU/A ASP/FU LV/FU INC I 63 21000. 0. 1.00 21000. 0. 21000. 320.0 65. 0. 65. 0.00 22. .069 943 943 0. 2 62 3000. 0. 1.00 3000. 0. 3000. 40.0 75. 0. 75. 0.00 2. .072 1034 1034 0. 3 63 2500. 0. 1.00 2500. 0. 2500. 40.0 62. 0. 62. 0.00 2. .051 1202 1202 0.4 61 19700. 0. 1.00 19700. 0. 19700. 320.0 61. 0. 61. 0.00 19. .061 995 995 0. 5 63 25000. 0. 1.00 25000. 0. 25000. 320.0 78. 0. 78. 0.00 23. .072 1077 1077 0.6 60 6000. 0. 1.00 6000. 0. 6000. 160.0 37. 0. 37. 0.00 11. .072 517 517 0. 7 59 30000. 0. 1.00 30000. 0. 30000. 480.0 62. 0. 62. 0.00 33. .069 900 900 0.8 63 38000. 0. 1.00 38000. 0. 38000. 480.0 79. 0. 79. 0.00 19. • 040 1973 1973 0.9 61 35640. 0. 1.00 35640. 0. 35640. 440.0 81. 0. 81. 0.00 24. .056 1433 1433 0. 10 61 23625. 0. 1.00 23625. 0. 23625. 320.0 73. 0. 73. 0.00 22. .070 1051 1051 0. 11 58 14800. 0. 1.00 14800. 0. 14800. 320.0 46. 0. 46. 0.00 20. .063 733 733 0.12 61 16000. 0. 1.00 16000. 0. 16000. 320.0 50. 0. 50. 0.00 2 .059 844 844 0. 13 62 12000. 0. 1.00 12000. 0. 12000. 240.0 50. 0. 50. 0.00 12. .050 998 998 0.14 61 7480. 0. 1.00 7480. 0. 7480. 160.0 46. 0. 46. 0.00 7. .044 1045 1045 o. 15 59 12800. 0. 1.00 12800. 0. 12800. 160.0 80. 0. 80. 0.00 11. .069 1157 1157 0. 16 62 36500. 0. 1.00 36500. 0. 36500. 480.0 76. 0. 76. 0.00 31. • 066 1151 1151 0.17 61 25600. 0. 1.00 25600. 0. 25600. 320.0 80. 0. 80. 0.00 21. .066 1197 1197 o.18 59 12800. 0. 1.00 12800. 0. 12800. 160.0 80. 0. 80. 0.00 11. .072 1103 1103 0. 19 61 5200. 0. 1.00 5200. 0. 5200. 160.0 32. 0. 32. 0.00 5. .032 993 993 0. 20 61 24000. 0. 1.00 24000. 0. 24000. 240.0 100. 0. 100. 0.00 17. .072 1379 1379 o.21 63 62419. 0. 1.00 62419. 0. 62419. 780.0 80. 0. 80. 0.00 51. .066 1203 1203 0. 22 63 18580. 0. 1.00 18580. 0. 18580. 235.0 79. 0. 79. 0.00 15. .064 1234 1234 0.23 65 48000. 0. 1.00 48000. 2400. 45600. 480.0 95. 5. 100. 0.00 34. .072 1379 1310 0.24 65 32000. 0. I.OC 32000. 0. 32000. 320.0 100. 0. 100. 0.00 22. .069 1447 1447 0. 25 64 15400. 0. 1.00 15400. 0. 15400. 154.0 100. 0. 100. 0.00 11. .072 1379 1379 o.26 63 34000. 0. 1.00 34000. 0. 34000. 400.0 85. 0. 85. 0.00 25. .063 1330 1330 0.27 64 110000. 0. 1.00 110000. 20000. 90000. 2180.0 41. 9. 50. 0.00 70. .032 1549 1267 0. 28 61 11100. 0. 1.00 11100. 0. 11100. 160.0 69. 0. 69. 0.00 10. • 066 1051 1051 0. 29 62 9000. 0. 1.00 9000. 0. 9000. 160.0 56. 0. 56. 0.00 7. .048 1156 1156 0.30 63 16000. 0. 1.00 16000. 0. 16000. 320.0 50. 0. 50. 0.00 12. .040 1243 1243 0. 31 63 23000. 0. 1.00 23000. 3732. 19268. 320.0 60. 11. 71. 0.00 17. .055 1289 1080 0. 32 59 42250. 0. 1.00 42250. 2650. 39600. 640.0 61. 4. 66. 0.00 34. .053 1238 1160 o.33 59 91525. 0. 1.00 91525. 1505. 90020. 1286.0 70. I. 71. 0.00 93. .072 975 959 0. TOTAL NO. OF FARMS * 33 AVERAGE ASP/FU * 1157. AVERAGE LV/FU = 1138. NO ASSESSMENT VALUES GIVEN NO INCOME VALUES GIVEN STATISTICAL ANALYSIS Y VAR * ASP/A X VAR = FU/A REGRESSION EQUATION Y = 18.04 + 846.01 X RSQ = .3344 SY * 17.86 YAVE = 69.62 SB = 214.36 R = .5782 SYX » 14.80 XAVE * .060 T = 3.94 SOURCE DF SS HS F DUE TO REG I .34150213E+04 •34150213E+04 15.57 ABOUT REG 31 •6797I566E+04 .21 26311E+03 TOTAL 32 .10212198E+05 +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + 0.000 +  + + + +  + + + 0.000 0.000 0.000 0.000 +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + +  + + + INCR 122 APPRAISAL DATA FOR R• J. REMER * BOZEMAN, MONT. - WHEAT FARMS - GLENDIVE DIST • NAME/NO. YR SALE P ASV TFR ASP BLDV LANDV ACRT LV/A BV/A ASP/A ASR FU FU/A ASP/FU LV/FU INC INCR I 63 21000. 0. 1.15 24150. 0. 24150. 320.0 75. 0. 75. 0.00 22. .069 1085 1085 0. 0.0002 62 3000. 0. 1.20 3600. 0. 3600. 40.0 90. 0. 90. 0.00 2. .072 1241 1241 0. 0.0003 63 2500. 0. 1.15 2875. 0. 2875. 40.0 71. 0. 71. 0.00 2. .051 1383 1383 0. 0.0004 61 19700. 0. 1.25 24625. 0. 24625. 320.0 76. 0. 76. 0.00 19. .061 1244 1244 0. 0.0005 63 25000. 0. 1.15 28750. 0. 28750. 320.0 89. 0. 89. 0.00 23. .072 1239 1239 0. 0.0006 60 6000. 0. 1.30 7800. 0. 7800. 160.0 48. 0. 48. 0.00 11. .072 672 672 0. 0.0007 59 30000. 0. 1.35 40500. 0. 40500. 480.0 84. 0. 84. 0.00 33. .069 1215 1215 0. 0.0008 63 38000. 0. 1.15 43700. 0. 43700. 480.0 91. 0. 91. 0.00 19. .040 2269 2269 0. 0.0009 61 35640. 0. 1.25 44550. 0. 44550. 440.0 101. 0. 101. 0.00 24. .056 1792 1792 0. 0.00010 61 23625. 0. 1.25 29531. 0. 29531. 320.0 92. 0. 92. 0.00 22. .070 1314 1314 0. 0.00011 58 14800. 0. 1.40 20720. 0. 20720. 320.0 64. 0. 64. 0.00 20. .063 1026 1026 0. 0.00012 61 16000. 0. 1.25 20000. 0. 20000. 320.0 62. 0. 62. 0.00 18. .059 1055 1055 0. 0.00013 62 12000. 0. 1.20 14400. 0. 14400. 240.0 60. 0. 60. 0.00 12. .050 1197 1197 0. 0.00014 61 7480. 0. 1.25 9350. 0. 9350. 160.0 58. 0. 58. 0.00 7. .044 1306 1306 0. 0.00015 59 12800. 0. 1.35 17280. 0. 17280. 160.0 108. 0. 108. 0.00 11. .069 1562 1562 0. 0.00016 62 36500. 0. 1.20 43800. 0. 43800. 480.0 91. 0. 91. 0.00 31. • 066 1381 1381 0. 0.00017 61 25600. 0. 1.25 32000. 0. 32000. 320.0 100. 0. 100. 0.00 21. • 066 1496 1496 0. 0.00018 59 12800. 0. 1.35 17280. 0. 17280. 160.0 108. 0. 108. 0.00 11. .072 1489 1489 0. 0.00019 61 5200. 0. 1.25 6500. 0. 6500. 160.0 40. 0. 40. 0.00 5. .032 1242 1242 0. 0.00020 6 I 24000. 0. 1.25 30000. 0. 30000. 240.0 125. 0. 125. 0.00 17. .072 1724 1724 0. 0.00021 63 62419. 0. 1.15 71781. 0. 71781. 780.0 92. 0. 92. 0.00 51. • 066 1383 1383 0. 0.00022 63 18580. 0. 1.15 21367. 0. 21367. 235.0 90. 0. 90. 0.00 15. .064 1419 1419 0. 0.00023 65 48000. 0. 1.05 50400. 2400. 48000. 480.0 100. 5. 105. 0.00 34. .072 1448 1379 0. 0.00024 65 32000. 0. 1.05 33600. 0. 33600. 320.0 105. 0. 105. 0.00 22. .069 1520 1520 0. 0.00025 64 15400. 0. 1.10 16940. 0. 16940. 154.0 HO. 0. 110. 0.00 11. .072 1517 1517 0. 0.00026 63 34000. 0. 1.15 39100. 0. 39100. 400.0 97. 0. 97. 0.00 25. .063 1529 1529 0. 0.00027 64 110000. 0. 1.10 121000. 20000. 101000. 46. 9. 55. 0.00 70. .032 1704 1422 0. 0.00028 61 11100. 0. 1.25 13875. 0. 13875. 160.0 86. 0. 86. 0.00 10. • 066 1313 1313 0. 0.00029 62 9000. 0. 1.20 10800. 0. 10800. 160.0 67. 0. 67. 0.00 7. .048 1387 1387 0. 0.00030 63 16000. 0. 1.15 18400. 0. 18400. 320.0 57. 0. 57. 0.00 12. .040 1430 1430 0. 0.00031 63 23000. 0. 1.15 26450. 3732. 22718. 320.0 70. 11. 82. 0.00 17. .055 1482 1273 0. 0.00032 59 42250. 0. 1.35 57037. 2650. 54387. 640.0 84. 4. 89. 0.00 34. .053 1671 1593 0. 0.00033 59 91525. 0. 1.35 123558. 1505. 122053. 1286.0 94. I. 96. 0.00 93. .072 1317 1301 0. 0.000 TOTAL NO. OF FARMS = 33 AVERAGE ASP/FU = 1395. AVERAGE LV/FU = 1376. NO ASSESSMENT VALUES GIVEN NO INCOME VALUES GIVEN STATISTICAL ANALYSIS Y VAR = ASP/A X VAR = FU/A REGRESSION EQUATION Y = 18.99 + 1068.40 X RSO = .4218 SY = 20.08 YAVE = 84.12 SB = 224.63 R = .6495 SYX = 15.51 XAVE = .060 T = 4.75 SOURCE DF SS MS F DUE TO REG I • 54464446E+04 • 54464446E+04 22.62 ABOUT REG 31 •74635710E+04 .24 76035E+03 TOTAL 32 •12910051E+05 123 APPRAISAL DATA FOR R. J. REMER , BOZEMAN , MONT. - LVSTK RANCHES - ISLENDIVE D 1ST. NAME/NO. YR SALE P ASV TFR ASP BLDV LANDV ACRT LV/A BV/A ASP/A ASR AUR AUH AUT A/AU ASP/AU INC INCR I 64 45000. 0. 1.00 45000. 0. 45000. 2520.0 17.85 0. 17.85 0.00 40 0 33 74.4 1328 0. 0 ooo2 63 28200. 0. 1.00 28200. 0. 28200. 1880.0 15.00 0. 15.00 0.00 47 O 39 48.0 720 o.3 63 3800. 0. 1.00 3800. 0. 3800. 320.0 11.87 0. 11.87 0.00 8 O 6 48.0 570 0. 0*0004 64 1600. 0. 1.00 1600. 0. 1600. 320.0 5.00 0. 5.00 0.00 6 O 5 55.2 276 0. 0*0005 64 3000. 0. 1.00 3000. 0. 3000. 320.0 9.37 0. 9.37 0.00 9 O 8 39.6 371 0*0006 63 1850. 0. 1.00 1850. 0. 1850. 154.1 12.00 0. 12.00 0.00 2 O I 92.4 1110 0* 0*0007 62 127500. 0. 1.00 127500. 20000. 107500. 4200.0 25.59 4. 30.35 0.00 84 169 240 17.4 531 o. 0*0008 63 75000. 0. 1.00 75000. 0. 75000. 3750.0 20.00 0. 20.00 0.00 82 31 100 37.1 743 0. O OOO10 64 18000. 0. 1.00 18000. 0. 18000. 600.0 30.00 0. 30.00 0.00 14 15 27 21.7 651 0. 0*00013 63 7500. 0. 1.00 7500. 750. 6750. 150.0 45.00 5. 50.00 0.00 3 18 20 7.2 36015 64 51200. 0. 1.00 51200. 0. 51200. 633.0 80.88 0. 80.88 0.00 12 25 35 17.7 1437 0 *16 64 18000. 0. 1.00 18000. 0. 18000. 801.0 22.47 0. 22.47 0.00 17 13 27 28.7 646   0.000 TOTAL NO. OF RANCHES = 12 AVERAGE ASP/AU = 728. GENERAL GRAZING PD. = 10.0 ♦SPECIAL GRAZING PD. NO ASSESSMENT VALUES GIVEN NO INCOME VALUES GIVEN STATISTICAL ANALYSIS Y VAR = ASP/A X VAR = FU/A REGRESSION EQUATION Y = 47.07 -.53 X RSQ = .3913 R = -.6255 SOURCE DUE TO REG ABOUT REG TOTAL SY SYX DF I 10 11 21.25 17.38 YAVE XAVE 25.40 40.646 SB T SS .19439109E+04 .30236264E+04 .49675377E+04 MS .I9439109E+04 •30236264E+03 .21 -2.53 F 6.42 124 APPRAISAL DATA FOR R • J. REMER , BOZEMAN , MONT. - LVSTK RANCHES - 'GLENDIVE DI ST. NAME/NO. YR SALE P ASV TFR ASP BLDV LANDV ACRT LV/A BV/A ASP/A ASR AUR AUH AUT A/AU ASP/AU INC INCR I 64 45000. 0. 1.12 50400. 0. 50400. 2520.0 20.00 0. 20.00 0.00 40 O 33 74.4 1488 0. n nnn--2-------- -63-— 28 200. O. IiiO 33276. 0. 33276. 1880.0 17.70 0. 17.70 0.00 47 O 39 48.0 849 0. f) nno 3 63 3800. 0. 1.18 4484. 0. 44 84. 320.0 14.01 0. 14.01 0.00 8 O 6 48.0 672 0. n f)(iQ ”4 - 64 1600. 0. 1.12 1792. 0. 1792. 320.0 5.60 0. 5.60 0.00 6 O 5 55.2 309 0. n nnn 5 64 3000. 0. 1.12 3360. 0. 3360. 320.0 10.50 0. 10.50 0.00 9 O 8 39.6 415 0. o noo "63 1830; Ti TO 2103. 0. 2183. 154.1 14.16 0. 14.16 0.00 2 O I 92.4 1309 0. n nnn 7 62 127500. 0. 1.24 158100. 20000. 138100. 4200.0 32.88 4. 37.64 0.00 84 169 240 17.4 658 0.--g.----- 63 75000. ---1.1*— 00500. 0. 88500. 3750.0 23.60 0. 23.60 0.00 82 31 100 37.1 877 0.10 64 18000. 0. 1.12 20160. 0. 20160. 600.0 33.60 0. 33.60 0.00 14 15 27 21.7 729 0. -- ---------- -63* 7500; ---I-to — — OOSOi 750. 8100. 150.0 54.00 5. 59.00 0.00 3 18 20 7.2 425 0. 15 64 51200. 0. 1.12 57344. 0. 57344. 633.0 90.59 0. 90.59 0.00 12 25 35 17.7 1609 0.-Jr6----- -64 ioooo.- fr. 1.12 201*0. ---Oi— 20160. 801.0 25.16 0. 25.16 0.00 17 13 27 28.7 723 0. 0.000 AVERAGE ASP/AU = ♦SPECIAL GRAZING PD. NO INCOME VALUES GIVEN 839. tfl.O MO." I STATISTICAL ANALYSIS Y VAR = ASP/A FU/A REGRESSION EQUATION RSQ .4091 24.07 YAVE XAV€- 29.29 -40.646 SB T .23 -2.63 I --SOURCE------ BF-------- SS---- —....... -HS' F DUE TO REG I .2608121IE+04 .26081211E+04 6.92 ABOUT--REO----- tO--.37671009C-XH- .376710896+03 TOTAL 11 .63752302E+04 125 APPRAISAL DATA FOR J. HEIN, GLENDIVE, MONT. - PROJ. NO. IIG94-3(9>76 FARM SALES NAMEZNO. YR SALE P ASV TFR ASP BLDV LANDV ACRT LVZA BVZA ASPZA ASR FU FUZA ASPZFU LVZFU INC INCR I 64 17000. 0. 1.00 17000. 0. 17000. 83.0 204. 0. 204. 0.00 52. • 628 326 326 0. 0.0002 63 110000. 0. 1.00 110000. 0. 110000. 1418.0 77. 0. 77. 0.00 238. .167 462 462 0. 0.0003 60 51000. 0. 1.00 51000. 0. 51000. 794.0 64. 0. 64. 0.00 88. • 111 575 575 0. 0.0004 64 12000. 0. 1.00 12000. 0. 12000. 120.0 100. 0. 100. 0.00 45. .376 265 265 0.5 60 14000. 0. 1.00 14000. 0. 14000. 151.0 92. 0. 92. 0.00 52. .349 265 265 0. O 000N 6 60 10500. 0. 1.00 10500. 1000. 9500. 234.0 40. 4. 44. 0.00 9. .038 1153 1043 0. 0 000 7 61 20000. 0. 1.00 20000. 0. 20000. 720.0 -27. 0. 27. 0.00 41. .057 485 485 0. O 0008 64 110000. 0. 1.00 110000. 8100. 101900. 3713.0 27. 2. 29. 0.00 102. .027 1072 993 0. O 0 OO9 65 18000. 0. 1.00 18000. 0. 18000. 635.0 28. 0. 28. 0.00 8. .013 2107 2107 0. O OOO10 61 45000. 0. 1.00 45000. 4140. 40860. 481.0 84. 8. 93. 0.00 93. .194 481 437 0. O OOO11 65 45000. 0. 1.00 45000. 3425. 41575. 766.0 54. 4. 58. 0.00 93. .121 483 446 0. O OOO12 65 69000. 0. 1.00 69000. 4375. 64625. 575.0 112. 7. 120. 0.00 131. • 228 525 492 0. O O OO13 60 37000. 0. 1.00 37000. 9400. 27600. 303.0 91. 31. 122. 0.00 69. .229 532 397 0. O ooo14 64 50000. 0. 1.00 50000. 2180. 47820. 800.0 59. 2. 62. 0.00 112. .140 444 425 0. 0* 0 0 015 64 26400. 0. 1.00 26400. 11000. 15400. 640.0 24. 17. 41. 0.00 16. .026 1583 923 0. 0*00016 65 18000. 0. 1.00 18000. 1475. 16525. 151.0 109. 9. 119. 0.00 39. .261 455 418 o. 0* 0 0 017 65 36000. 0. 1.00 36000. 0. 36000. 414.0 86. 0. 86. 0.00 120. .291 297 297 o. 0 00018 63 45000. 0. 1.00 45000. 11000. 34000. 157.0 216. 70. 286. 0.00 113. .723 396 299 0. o *ooo19 64 75000. 0. 1.00 75000. 9850. 65150. 377.7 172. 26. 198. 0.00 226. .598 331 288 0. 0*00020 63 15000. 0. 1.00 15000. 3000. 12000. 87.0 137. 34. 172. 0.00 42. .489 352 281 0 * 0 0 021 64 130000. 0. 1.00 130000. 8160. 121840. 4549.0 26. I. 28. 0.00 171. .037 758 710 ol 0.000 TOTAL NO. OF FARMS = 21 AVERAGE ASP/FU = 636. AVERAGE LV/FU = 568. NO ASSESSMENT VALUES GIVEN NO INCOME VALUES GIVEN STATISTICAL ANALYSIS Y VAR = ASP/A X VAR = FU/A REGRESSION EQUATION Y = 23.34 ♦ 307.10 X RSQ = .9164 SY = 68.55 YAVE = 98.11 SB = 21.27 R s .9573 SYX = 20.33 XAVE = .243 T = 14.43 SOURCE DF SS MS F DUE TO REG I •86153492E+05 .86153492E+05 208.38 ABOUT REG 19 .78551917E+04 .41343114E+03 TOTAL 20 .94008684E+05 126 APPRAISAL DATA FOR J. HEIN, GLENDlVE, MONT. - PROJ. NO. 11694-3(9)76 APPRAISALS NAME/NO. YR APPR V ASV TFR ADJ APPRV BLDV LANDV ACRT LV/A BV/A APV/A ASR FU FU/A APV/FU LV/FU INC INC I 65 35000. 0. 1.00 35000. 520. 34480. 640.0 53. 0. 54. 0.00 54. .085 638 628 0. 0.000 2 65 138700. 0. 1.00 138700. 20290. 118410. 2920.0 40. 6. 47. 0.00 152. .052 907 774 0. 0.000 3 65 46000. 0. 1.00 46000. 3120. 42880. 766.0 55. 4. 60. 0.00 88. .115 520 485 0. 0.000 4 65 103000. 0. 1.00 103000. 8400. 94600. 665.0 142. 12. 154. 0.00 322. .485 318 292 0. 0.000 5 65 61000. 0. 1.00 61000. 9650. 51350. 358.0 143. 26. 170. 0.00 142. .398 427 360 0. 0.000 6 65 86400. 0. 1.00 86400. 9600. 76800. 480.0 160. 20. 180. 0.00 210. .438 410 364 0. 0.000 7 65 52000. 0. 1.00 52000. 8000. 44000. 800.0 55. 10. 65. 0.00 90. .113 573 484 0. 0.000 8 65 11200. 0. 1.00 11200. 2200. 9000. 160.0 56. 13. 70. 0.00 18. .115 603 484 0. 0.000 10 65 67875. 0. 1.00 67875. 11850. 56025. 1086.0 51. 10. 62. 0.00 95. .087 710 586 0. 0.000 11 65 10530. 0. 1.00 10530. 1040. 9490. 234.0 40. 4. 45. 0.00 7. .031 1447 1304 0. 0.000 TOTAL NO. OF FARMS = IO AVERAGE APV/FU = 655. AVERAGE LV/FU = 576.__________________ NO INCOME VALUES GIVEN STAIiSIlLAL ANALYSIS Y VAR = ASP/A X VAR = FU/A REGRESSION EQUATION Y = 32.63 + 303.25 X RSQ = .9539 SY = 54.28 YAVE * 91.00 SB = 23.55 R = .9767 SYX = 12.35 XAVE = .192 T = 12.87 SOURCE______ DF________ SS ___ MS______________ F__ DUE TO REG I .25298649E+05 .25298649E+05 165.79 ABOUT REG 8 .12207039E+04 .15258798E+03 TOfAL 9 .26519379E+05 127 APPRAISAL DATA FOR R. J. REMERf BOZEMAN, MONT. - IRR. FARMS - G. FALLS DIST NAME/NO. YR SALE P ASV TFR ASP BLDV LANDV ACRT LV/A BV/A ASP/A ASR FU FU/A ASP/FU LV/FU INC INCR I 63 32000. 0. 1.00 32000. 0. 32000. 274.0 116. 0. 116. 0.00 108. .396 294 294 0. 0.0002 60 35000. 0. 1.00 35000. 0. 35000. 274.0 127. 0. 127. 0.00 121. .442 288 288 0. 0.000 3 62 40000. 0. 1.00 40000. 0. 40000. 307.0 130. 0. 130. 0.00 191. .625 208 208 0. 0.0004 61 19000. 0. 1.00 19000. 0. 19000. 208.0 91. 0. 91. 0.00 102. .490 186 186 0. 0.0005 63 16000. 0. 1.00 16000. 0. 16000. 160.0 100. 0. 100. 0.00 67. .421 237 237 0. 0.0006 60 38550. 0. 1.00 38550. 0. 38550. 543.0 70. 0. 70. 0.00 362. . 666 106 106 0. 0.000 7 63 20000. 0. 1.00 20000. 0. 20000. 637.0 31. 0. 31. 0.00 52. .081 383 383 0. 0.0008 63 3100. 0. 1.00 3100. 0. 3100. 19.0 163. 0. 163. 0.00 15. .833 195 195 0. 0.0009 61 25000. 0. 1.00 25000. 0. 25000. 274.0 91. 0. 91. 0.00 154. .564 161 161 0. 0.000 IO 61 14700. 0. 1.00 14700. 0. 14700. 152.0 96. 0. 96. 0.00 80. .531 181 181 0. 11 65 35000. 0. 1.00 35000. 0. 35000. 412.0 84. 0. 84. 0.00 91. .223 380 380 0. 0.00012 64 30000. 0. 1.00 30000. 0. 30000. 332.0 90. 0. 90. 0.00 84. .255 353 353 0. 0.000 13 63 5000. 0. 1.00 5000. 0. 5000. 31.0 161. 0. 161. 0.00 16. .545 295 295 0. 0.000 TOTAL NO. OF FARMS = 13 AVERAGE ASP/FU = 251. AVERAGE LV/FU = 251. NO ASSESSMENT VALUES GIVEN NO INCOME VALUES GIVEN I I STATISTICAL ANALYSIS Y VAR * ASPZA X VAR = FUZA REGRESSION EQUATION Y = 49.78 + 116.64 X RSQ = .4210 SY = 35.93 YAVE = 104.32 SB = 41.24 R - .6488 SYX = 28.56 XAVE = .467 T = 2.82 SOURCE DF SS MS F DUE TO REG I •65258581E+04 .65258581E+04 7.99 ABOUT REG 11 .89743660E+04 .81585145E+03 TOTAL 12 .15500203E+05 128 APPRAISAL DATA FOR R • J . REMER r BOZEMAN, MONT. - IR R • FARMS - G. FALLS DIST NAME/NO. YR SALE P ASV TFR ASP BLOV LANDV ACR T LV/A BV/A ASP/A ASR FU FUXA ASP/FU LV/FU INC INCR I 63 32000. 0. 1.12 35840. 0. 35840. 274.0 130. 0. 130. 0.00 108. .396 329 329 0. n nnn --- 2-------- 60 35000. 0. 1.24 43400. 0. 43400. 274.0 158. 0. 158. 0.00 121. .442 357 357 0. 3 62 40000. 0. 1.16 46400. 0. 46400. 307.0 151. 0. 151. 0.00 191. .625 241 241 0. 0.000 ---4— 61 19000. 0. 1.20 22800. 0. 22800. 208.0 109. 0. 109. 0.00 102. .490 223 223 0. 5 63 16000. 0. 1.12 17920. 0. 17920. 160.0 112. 0. 112. 0.00 67. .421 265 265 0. o noo