The normalized interval regression model with outlier detection and its real-world application to house pricing problems

Tanaka and his colleagues initially proposed fuzzy linear regression models in 1982. From then on, fuzzy regression analysis has been widely studied by many researchers. Since Tanaka's model uses the inclusion relationship between the given data and the estimated data, it was pointed out that Tanaka's model is sensitive to outliers. How to deal with the outlier problem has been a very important issue and attracted much attention from fuzzy regression researchers. Given crisp multiple independent variables and single interval dependent variable, we introduce the normalized upper and lower interval regression models and propose two outlier detection approaches for them. The dual problem of the normalized upper interval regression model is used to find out potential outliers. For the normalized lower interval regression model, the existence of the outliers makes it infeasible. The relaxation approach is proposed to find out the outliers. By deleting the outliers, we can find out the possibilistic functional relationship of the major data. A case study involving a house pricing problem is analyzed in detail. Household size, loan ratio and annual household income are identified as the independent variables and acceptable purchase price is the interval dependent variable. With the data collected from the survey in Shanghai, the normalized upper and lower interval regression models are built with deleting the outliers. The proposed models provide managerial insights into the real estate market and important policy implications in regulating urban land development.