Statistical Modelling of the Market Value of Dwellings, on the Example of the City of Kraków

Abstract

The analysis of a city’s spatial development, in terms of a location that meets the needs of its inhabitants, requires many approaches. The preliminary assessment of the collected material showed that there was real estate in the database whose price did not have market characteristics. For the correct formulation of the valuation model, it is necessary to detect and eliminate or reduce the impact of these properties on the valuation results. In this study, multivariate analysis was used and three methods of detecting outliers were verified. The database of 8812 residential premises traded on the primary market in Kraków was analyzed. In order to detect outliers, the following indices were determined: projection matrix, Mahalanobis distances, standardized chi test and Cook distances. Critical values were calculated based on the formulas proposed in the publication. The probability level was P = 0.95. The article shows that the selected methods of eliminating outliers—the methods of standardized residuals and the Cook’s distance method give similar regression models. Further analysis (with the use of classification tree methods) made it possible to distinguish zones that are homogeneous in terms of price dispersion. In these zones, a set of features influencing real estate prices were determined.