Modeling Cross Sectional Data Using Fuzzy Regression Analysis: A Case Study of Value Price of Residential Properties in Ames

Abstract

Fuzzy regression analysis (FRA), also known as non-statistical regression analysis, is an approach used to establish relationship between an input and output variables that are fuzzy. Fuzzy regression analysis serves as an alternative method to classical regression analysis (CRA). The models 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 leading to non normality, heteroscedasticity and non normality in the data. Thus, fuzzy regression analysis gives a solution to challenges that may arise when using statistical regression models. Because of the uncertainties that may arise in a given data, the model was based on cross sectional data for the price of residential properties sold in Ames Iowa. Since the price of residential properties fluctuates, the model was developed in three forms. Three fuzzy regression methods; possibilistic linear regression with least squares (PLRLS), possibilistic linear regression (PLR) and fuzzy least absolute residuals (FLAR) methods were used to fit the fuzzy linear regression model (FLRM). In this study lot area, total basement area square feet and garage area were selected as explanatory variables. The results show that by applying different fuzzy regression methods to model the data, fuzzy least squares methods yielded significant results for modelling the value of the residential properties.