A Comprehensive Statistical Analysis of Residential Property Valuation Using Multiple Linear Regression Techniques

Abstract

This research paper presents a comprehensive statistical analysis of residential property valuation in King County, Washington, employing Multiple Linear Regression (MLR) as the primary analytical framework. Utilizing a dataset comprising 21,613 residential property transactions recorded between May 2014 and May 2015, this study examines how structural, locational, and qualitative property attributes jointly determine sale prices. The dataset encompasses 21 variables including living area square footage, number of bedrooms and bathrooms, property grade, condition, waterfront access, view quality, and proximity-based neighborhood features.

Two regression models were developed and evaluated: a standard MLR model and a log-transformed variant for price normalization. The standard MLR model achieved an R² of 0.6526 and an adjusted R² of 0.6514, with a Root Mean Square Error (RMSE) of $229,186, while the log-transformed model produced an R² of 0.6554 and adjusted R² of 0.6543. Key findings reveal that property grade (r = 0.667), living area (r = 0.702), and waterfront status (β = $554,704) are the strongest determinants of residential value. Multicollinearity diagnostics using Variance Inflation Factors (VIF), Durbin-Watson statistics (DW = 2.008), and residual normality tests were conducted to validate model integrity. The study concludes that while MLR provides robust interpretable predictions, log-transformation addresses price skewness (skew = 4.024) and improves distributional assumptions.