Predict house prices using quantile regression
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Quantile Regression Model (QRM), introduced by Koenker and Bassett in 1978, is a well-established and widely used technique in theoretical and applied statistics. QRM is a natural extension of the traditional OLS regression model and it is advantageous over the traditional techniques in several aspects: (1) QRM is robust to outliers, non-normal errors and heteroscedasticity; (2) It allows researchers to study the impact of predictors on different quantiles of response variable, not merely its conditional mean. Due to these advantages, QRM is applied in various fields such as risk measurement in finance, and fat-tailed distributions such as if cheaper food cause obesity. The current research paper aims at applying QRM in an open source housing data with 79 house-related features and 1460 cases, and comparing its predictive performance with the OLS model. The article also extends the QRM to Bayesian Quantile Regression and Quantile Random Forest to further explore the application performance of quantile models. The results indicate that all the quantile models outperformed the OLS regression in prediction at the 0.5th quantile and the 0.75th quantile based on RMSE. In general, most estimates derived by QRM and BQR show consistency across quantiles. Quantile Random Forest show similar variable selection results comparing with LASSO, but slightly higher RMSE than the other quantile models.