MODELING CROSS SECTIONAL DATA OF THE SALE PRICE OF RESIDENTIAL PROPERTIES IN AMES USING FUZZY REGRESSION ANALYSIS

Abstract

Fuzzy Regression Analysis (FRA), also known as non-statistical regression analysis, is an ap proach used to establish an ambiguous connection between input and output variables. FRA serves as an alternative method to classical Regression Analysis CRA. The models that are used to model cross sectional data are statistical regression models which are based on linearity, normality and homoscedasticity assumptions. However, these assumptions may not hold true. Thus, fuzzy regression analysis gives a solution to challenges that may arise when using sta tistical regression models. The main objective of the study was modeling cross sectional data of the sale price of the residential properties in Ames using fuzzy regression analysis and the specific objectives were performing diagnostic tests on fuzzy regression assumptions, fitting the model of fuzzy linear regression and evaluating the fuzzy model of linear regression. Secondary data accessed from Ames assessors office was used. Data visualization indicated price fluctua tions of the residential properties which was uncertain. Diagnostic tests of normality, linearity, multicollinearity and homoscedasticity were performed to ascertain the application of fuzzy regression analysis. After verifying the assumptions, fuzzy regression analysis was applicable to model this application. Three fuzzy regression methods: possibilistic linear regression meth ods with least squares, possibilistic linear regression and fuzzy least absolute residuals were employed to fit the fuzzy linear regression model (FLRM). Fitting FLRM involved conversion of real value observations of the response variable into fuzzy numbers. The fitted models using fuzzy regression methods were assessed based on total fit error and goodness of fit measure. According to the study’s findings, method based on fuzzy least squares gave a better compati bility of the fuzzy linear regression model than possibilistic methods. Also, methods based on possibilistic regression indicated the range in which the price of the residential properties can vary to the smallest and largest value using predictor variables present. Therefore, to model cross sectional data of the price of residential properties which may change at a given time, models based on fuzzy least squares methods were preferred compared to possibilistic linear regression methods. The study recommended that diagnostic tests to be performed on any given data set to determine the model to be used when fitting the data, fuzzy linear regression models to be used to fit a given data that assumes classical regression assumptions and fuzzy least squares methods be used in modeling cross sectional data of the sale price of the residential properties for optimal results when making decisions on the range at which the sale price may range.