Multiple Linear Regression Model for Estimating the Price of a Housing Unit

Abstract

This paper uses the respective unit costs, over fifteen (15) years, of selected Housing Unit Major Components (HUMC): cement, iron rods, aluzinc roofing sheets, coral paint, wood and sand, to develop Multiple Linear Regression Model (MLRM) for determining Housing Unit Price (HUP) for one-bedroom and two-bedroom housing units. In the modeling, the Ordinary Least Squares (OLS) normality assumption which could introduce errors in the statistical analyses was dealt with by log transformation of the data, ensuring the data is normally distributed and there is no correlation between them. Minimisation of Sum of Squares Error method was used to derive the model coefficients. The resultant MLRM is:  Ŷ_{i MLRM} = (X^'X)^-1 X^'Y(x_i^') where X is the sample data matrix. The specific model for one-bedroom housing unit is log_e (HUP_MLRM)_1-Bed = 1.017 – 2.225 x 10^-5 x CC + 2.512 x 10^-6 x CS + 6.016 x 10^-4 x CIR  +  1.985 x  10^-4 x CR + 5.694 x 10^-4 x CP -7.437 x 10^-4 x CW and that for two-bedroom housing unit is log_e (HUP_MLRM)_2-Bed = 5.760 – 7.501 x 10^-7 x CC + 2.935 x 10^-6 x CS + 1.898 x 10^-3 x CIR  +  6.695 x 10^-4 x CR - 9.157 x 10^-3 x CP +6.136 x 10^-3 x CW, where CC, CS, CIR, CR, CP and CW are costs of the total quantity of cement, sand, iron rods, roofing, paint and wood respectively. The MLRM was validated by using it to estimate the known HUP in the 15.5th year. From the results, the percentage absolute deviations of the estimated HUP from the known HUP are 1.27% and 2.02% for one-bedroom and two-bedroom housing units respectively, which are satisfactory. The novel approach presented in this paper is a valuable contribution to the body of knowledge in modeling.

 

Keywords: Multiple Regression Analysis, Housing Unit Major Components, Housing Unit Price