Fitting a regression model and a multilevel model to the purchase price of apartments by locality, floor level and number of rooms

Abstract

The data analyzed in this dissertation consists of the purchase price of 65 apartments from four localities in different parts of Malta. These properties were constructed from Government funds and their purchase price was quoted by the Government. These prices are normally less than those offered by speculators and are intended to help Maltese people with a limited income to own their house. Although these prices are somewhat controlled, we observed some interesting contrasts between the prices offered in different localities at different floor levels. The selected four localities in Malta are Pembroke, Naxxar, San Pawl and Qrendi. The aim of this study is to see how the mean price differs with locality, the number of rooms, and the floor level in which the apartment stands. The quoted price is the original price, without any reduction affected by the Government for those with a low income. In analyzing this data set, the purchase price is declared as the response variable, locality and floor levels are declared as factors and the number of rooms as a covariate. After checking the linearity and normality assumptions, it was an obvious choice to use regression analysis in analyzing this data set. ANOVA and ANCOVA models were used depending on the type of predictors used in the model. An alternative approach is to use a two level random intercept model in which the apartments are nested within localities. This multilevel analysis with a nesting structure includes unexplained variability at each level of nesting. This variability is not adequately explained by a regression model.