Analysis of Property Data Relating to Residential Subdivision - Term Paper Example

Table of Contents Table of Contents 1 EXECUTIVE SUMMARY 2 INTRODUCTION 2 “ANALYSIS OF PROPERTY DATA” – RESIDENTIAL SUBDIVISION 3 GENERAL FINDINGS ABOUT THE LOTS 4 “Generation of the Model and its Representation” 4 METHODOLOGY 5 RESULTS and the ANALYSIS 6 MODEL RELIABILITY 8 Advantages of using a regression model for predicting property prices 8 Disadvantages of using a regression model for predicting property prices 9 RECOMMENDATION 11 CONCLUSION 12 REFERENCES 14 Analysis of Property Data relating to Residential Subdivision EXECUTIVE SUMMARY Analysis of property data relating to residential-subdivision is a demanding task, using diverse variables like area, frontage, depth, shape, view, topography, and aspect of soil condition either filled or natural. Since they are variables of diverse nature, this report presents a different perspective to demonstrate their effect in the price of residential land using “multi-linear regression analysis”. A sample of 59 lots will be used to make the analysis and show that area, frontage and width of the lots are key price determinants of the lots and generally the residential land prices in the neighborhood. INTRODUCTION Regression analysis is a basic tool used in determining how changes in certain variables affect the value of a certain response variable called the dependent variable. It is largely concerned with estimating and or predicting the population mean or the average value of the dependent variable on the basis of known or fixed values of the explanatory variables (independent variables). This report will use the ‘multi-linear regression analysis model’ (MLRM). The model analyses the relationship existing between the list price or the sale price of the lots (dependent variables) and area, frontage, and width (independent variables). The regression will then attempt to fit the model to the observed data to help quantify the existing relationship between the two types of variables. The model fitted can then be employed in predicting new land prices (Carao and Hernandez 1992). “ANALYSIS OF PROPERTY DATA” – RESIDENTIAL SUBDIVISION This report makes a critical analysis of property data – residential subdivision of 59 lots. The report has also provided a profile of the lots by finding out the relevant central tendency that is, the mean, the median and the mode and dispersion which include the range, the average deviation (absolute mean deviation) and the standard deviation statistics for all the key variables relating to these lots. In addition, the report has used the data collected to establish a “multiple linear regression model (MLRM)” to predict the residential land prices in the neighborhood. The model used includes the following variables: area, frontage, width (independent variables) and the list price or the sale price of the lots (dependent variable). However, there are other variables that were found to have an influence the residential land prices though they have not been included in this model. These variables include depth, shape, view, topography, aspect and soil condition either filled or natural and many other factors. Nevertheless, they have been considered in making an informed conclusion about the residential land prices. The report have made a commentary on the reliability of the model by calculating the coefficient of multiple determination (R2) and then comparing the predicted results with the actual value of the data from the collected data. Prepare a report to advise your boss about your findings. In the report, there is an outline the advantages and disadvantages of using a regression model for predicting property prices (Chapin and Weiss 1962). GENERAL FINDINGS ABOUT THE LOTS Most of the lots are located mainly in the commuter zones or semi rural region which complies with the varied needs for residential apartments of the working population. This has really succeeded in decongesting the CBD. This report is important in that it find out the factors that are considered in determining the residential land prices in the neighborhood. The model used will help in the prediction of any other residential land price given that the factors considered remain constant in the period of the determination. This requires using the interconnected variables concurrently, that includes finding out a lot which provides the requirements of their potential buyers, economically enabled operations, and contribution to the welfare of the neighboring community. The processes of lot’s price prediction for residential subdivision can be simplified if property firm is provided with the tools that may help it in making decisions which are based on the knowledge and understanding of the environmental (variables) factors like the topography and the aspect of soil. The report looks for ways and means of involving the usefulness of Multiple Linear Regression Model, in predicting any residential land prices in the neighborhood with the crucial information collected (Chatterjee and Price 1977). The analysis established that the residential land price is largely determined by the area, frontage and width. “Generation of the Model and its Representation” The MLRA was used to determine the effect of each explanatory variable on a lot, thereby getting an equation which shows the coefficient (parameters) for the variables. Generation of regression-equation, in addition evaluates which independent variable significantly influence the regressand. In this report, the 59 lots are employed in the model set for prediction of residential land price wherein three variables are incorporated in the regression-analysis. The data collected was transformed using easy mathematical-functions as a necessity to get linearity of data-set which is in line with particular stochastic and other assumptions like “homoscedasticity”, no autocorrelation, no multicollinearity (the area, frontage, and width are not perfectly linearly correlated) and normal distribution (Dion 2002). METHODOLOGY The method that is employed in this report is the ordinary least square method of MLRA. In this method, it involved the finding of the values of the estimates b0, b1, b2, and b3 which will minimize the sum of the squares of the error value. Four variables are considered in this report. One of which is the dependent variable and the other three are the explanatory variables. In one MLRA the dependent variable was taken to be the list prices of all lots irrespective of whether it is sold or not. In the other analysis, the dependent variable was the list price of the unsold lots and the sale price of the sold lots. This report treated the lots which deposit has been taken as unsold and hence it used the list price in this case. The explanatory variables however, were not changed in the both cases. The explanatory (independent) variables considered in the analysis are; the area of the lots, the frontage and the width. In a multi-linear regression, when a scatter diagram is drawn and a linear trend fitted in the data not all the points will fall on the straight line because of the reasons outlined under; Imperfect specification of the functional form of the model Errors of aggregation Errors of measurement To account for this deviations of some values from the real figures the error term was introduced and whose introduction makes the functional model stochastic and since the error term could not be observed some assumptions about it were made (Mäler 1977). RESULTS and the ANALYSIS The analysis of the data established the findings as shown in the table below: Key variables mean median mode range Average deviation Standard deviation List price of the lots 505754.2373 $510,000 $515,000 101000 $13,282.96 97416.04447 Area of the lots 710.9118644 702.00 702.00 158.00 13.99258833 112.8733215 Frontage 6.093220339 6.12 6.32 1.04 0.304085038 4.554685966 width 19.77423729 19.17 18.00 9.40 1.599304798 13.71810408 From this analysis it can be seen that most of the lots are selling for $515,000 while the difference between the highly [priced lot and the least price is $101, 000. It is also clear that most of the lots are 702.00 M2 in size whereas the difference in size between the largest lot and the smallest is 158 M2. Similarly the average frontage and width of the lots is 6.09 and 19.77 respectively. Other important statistics from the model are shown in the table that follws Variable bi Intercept 227514.5882 X1 22650.38161 X2 4931149.593 X3 197.2479153 Based on this analysis a “multiple linear regression model” for prediction of residential land prices can thus be found to be Y = 227514.5882 + 22650.38161X1 + 4931149.593X2 + 197.2479153X3 Where, Y = the residential land price under prediction X1 = the frontage X2 = the width X3 = the area All the parameters of the model are positive indicating that there is a positive correlation between the residential land price and the variables under consideration. The intercept bo is positive showing that no residential land that can have no value. MODEL RELIABILITY The reliability of the model was determined through the use of the “coefficient of determination”. It measures the proportion of the variability of the dependent variable (the list price of the lots) that is explained by the variability of the independent variables (the area, the frontage, and the width). In the multiple analyses of the data using the list prices of all the lots it is established that 31% of the variation in the list price for all lots is explained by the size of the lot (area), the frontage and the width. The other 61% is explained by other variables apart from area, frontage and width. This is a clear case that there are a host of factors which determine the list price of the lots (Rosen 1974). Therefore based on these findings we cannot whole determine the price of the lot solely on this model. When we consider the list price of the unsold lots and the sale price of the sold lots the “coefficient of determination” is 27%. It does not improve either meaning that these three variables are not anyhow adequate to predict the residential land prices. It is only 27% of the variation in the list or sale price of the land that is explained by the area, frontage and width. The other percentage (63%) is explained by other variables beside the area, frontage and width. The decline in the reliability, however; can be due to the additional uncertainty in the sale price of the land. The sale price of the land has reduced and the reduction is not systematic from one lot to the other and thus the difference in the R2’s Advantages of using a regression model for predicting property prices Unlike the “Univariate regression”- one explanatory variable, the MLRA uses more than one predictor, which is usually sufficient in modeling property prices. “Multivariate regression” makes use of several predictive-variables concurrently, thereby modeling the price of the property in question with high accuracy. The use of many explanatory variables and a large sample size (number of observations) minimizes the variance of the property prices and consequently the reliability of the model used to determiner their price. Generally, typical suggestion for regression being a tool for predictive purposes may be that; Any time anyone can use simple performance in place of expensive and time-consuming tasks of comparing property prices and unhealthy bargaining. You can build a “response-surface-model” from the outcomes of some sample statistics, that is, describe with accuracy the reaction levels out of the figures obtained from a few restricted factors.   Disadvantages of using a regression model for predicting property prices Coming up with a regression-model entails the collection of explanatory and dependent variables data from a sample of property prices and their determinants, then fitting predetermined mathematical-relationship to the data collected (Tabuchi 1996). Once a regression-model is built, then the prediction of unknown property price (of the lot) can be determined. In addition, it is not practicable to use a small number of observations in MLRA. The number of observations should exceed the number of independent variables by at least two. Most of the demerits of the “multi-linear regression model analysis” comes from the various assumptions that are made in it’s applications especially when they do not hold. These include; Randomness of the error term. This assumption is violated when the errors exhibit a systematic pattern, for instance the price of the property can be rounded up to the nearest dollar amount. To ensure that this assumption is not violated all important explanatory variables should be included. In this case the location of the lots is also important in the determination of their prices and therefore it should have been included in the model. Assumption of the zero mean of the error term. If this assumption is not fulfilled, then the predictions of the property prices are biased. The solution is to ensure that all important explanatory variables that influence the price of the property are included in the model. Constant variance or the assumption of homoscedasticity. The consequences of not having a constant variance of the error term in all the prices of the property are; the estimators will still be unbiased but no minimum variance and the coefficients of standard errors will no longer be valid. This implies that the test of significance of the coefficients will not be valid and therefore any inference made could be misleading The error term is not normally distributed. If this holds the test of significance cannot be conducted since the test of significance is based on the normal distribution. The assumption of no autocorrelation. This is where the error term is not serially correlated. Note that heteroscedasticity is common when the data on property price is cross-sectional but serial correlation is common in time series property data. The price of the lots usually will keep appreciating with time since land is a fixed asset. The price can also go up merely due to time value of money and hence this model analysis if not refined cannot withstand the test of time. This will mainly occur due to The omission of important explanatory variables for property price Misspecification of the mathematical form of the model being used to predict property price Misspecification of the true random term Errors in the observation of the values of the both independent and dependent variables. For instance, someone may round down the dollar amount of the lot while another assessor might decide to truncate the indicated price of the lot to a whole dollar. Definitely, this will result to different values of the dependent variable. In the measurement of the frontage and the width of the lots, the observer may make a wrong observation of the calibration on the measuring tool and recordings of these kinds will bring inconsistency in the data. The explanatory variables will thus contain errors which will be transmitted to the inferences and the conclusions made. RECOMMENDATION The report recommends a further improvement of the model. A compassion analysis in relation to the approximated regression-coefficients of the residential land prices’ predictors may be made to improve the understanding and knowledge of the impacts of these variables to the regression-equation. This can enhance the application of the predictor-model to any lot price of similar characteristics. Since the regression-equation is dedicated to the price charged for a residential land, additional variables relating to the shape and topography of the lots can be integrated in this regression. Some other useful application of this MLRA is that resultant model may assist the mass-valuation-procedure, whereby the general-trend of the lots’ list can be simply pictured by any individual with inadequate experience in the sale of lots. An experienced evaluator can similarly use this model for scrutinizing the outcomes of his or her evaluation of a certain lot. Since the procedure of modeling is improved through further refinement, more applications in the determination of residential land prices can be made to improve its accuracy (Tamayo and Salvador 1990). CONCLUSION Using multi-linear regression, the factors area, frontage and width have been considered to influence the residential-subdivision prices of the lots. The area of the lot, the frontage and the width were all revealed to have positive correlation with lots’ prices. The variables were considered as predictors of lot prices with a reliability of 31% when the list prices for all the lots is considered and a reliability of 27% when the list price of unsold lots and the sale price of sold lots is considered. This outcome presents for the ability of the lot price prediction-equation in modeling the diverse variables that causes the difference among prices of the lots under consideration. In addition it was established in the report findings that regression-equation for estimating the price of the lot may be prepared to follow the economics of land theory. The report produced a regression-equation that relates the variables which determine the sale price of the lots with variables which describe environmental situation and the nature of the neighborhood. REFERENCES Carao, R., Hernandez, A. (1992). ‘Determinants of Urban Residential Land Values: Makati’, Quezon City: University of the Philippines. Chapin, F. S. and Weiss, S. F. (1962), “Factors influencing land development: an urban studies research monograph”. Chapel Hill: Chapel Hill Press. Chatterjee, S., Price, B. (1977), Regression Analysis by Example, New York: John Wiley & Sons. Dion, T. R. (2002). Land Development for Civil Engineers, New York: Wiley. Mäler, K. (1977). “A Note on the Use of Property Values in Estimating Marginal Willingness to Pay for Environmental Quality”, Journal of Environmental Economics and Management, 4:355–369. Rosen, S. (1974), “Hedonic Prices and Implicit Markets: Product Differentiation in Pure Competition”, The Journal of Political Economy, 82(1): 34 – 55. Tabuchi, T. (1996),”Quantity Premia in Real Property Markets’, Land Economics, 72(2): 206 – 217. Tamayo, G. E., Salvador, A. S. (1990). “A study on the determinants of urban residential real- property values”, Quezon City: University of the Philippines. Read More