Principal Components Regression Model for Estimating the Price of a Housing Unit
Abstract
This paper used the respective unit costs, over 15 years, of selected Housing Unit Major Components (HUMC): cement, iron rods, aluzinc roofing sheets, coral paint, wood and sand, to develop Principal Components Regression Model (PCRM) for determining Housing Unit Price (HUP) for one-bedroom and two-bedroom housing units. In developing the PCRM, the sample data (HUMC) was log transformed and bootstrapped; dimension reduction technique together with scree plots were used to determine the minimum number of principal components that explained the total variation in the sample data (HUP) for the PCRM. Principal Components Analysis method was used to derive the model coefficients. The resultant PCRM is: ŶiPCRM = βo+Ʃ pj=1 βj xi where βois the population parameter not associated to any predictive variable, βjare the estimated population parameters associated to the predictive variables and xi is the ith row predictive variables for validating the PCRM. The specific model for one-bedroom housing unit is loge(HUPPCRM)1-Bed = 10.866658 – 0.2 x10-4 x CC + 0.1 x 10-5x CS – 7.18 x 10-4x CIR – 2.37 x 10-4 x CR + 1.275 x 10-3 x CP + 2.48 x 10-4 x CW and that for two-bedroom housing unit is loge(HUPPCRM)2-Bed = 11.231345 + 0.7 x 10-5 x CC – 0.4 x 10-5 x CS – 1.182 x 10-3 x CIR – 1.54 x 10-4 x CR + 1.633 x 10-3x CP + 4.24 x 10-4 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 PCRM was validated by using it to estimate the known HUP in the 15.5 year. From the results, the percentage absolute deviations of the estimated HUP from the known HUP are 1.43% and 0.00 % for one- bedroom and two- bedroom housing units respectively, which are satisfactory. The approach presented in this paper is a valuable contribution to the body of knowledge in modeling.
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