Resistant measures in assessing the adequacy of regression models

Abstract

This research paper presents four median adequacy measures [resistant coefficient of determination (Rr2), resistant prediction coefficient of determination (pRr2), median square error prediction (MedSEP) and resistant modeling efficiency (MEr)] for assessing multiple regression models fitness and compares their effectiveness to their traditional mean adequacy measure equivalents (R2, pR2, MSEP and ME) in the presence of outliers or extreme data point. A multiple regression model of credit to agriculture (CTA), credit to manufacturing (CTM) and credit to export (CTE) on Gross Domestic Product (GDP) was fitted and assessed. Also, simulation at sample sizes of 36 and 100 for model without outliers and model with 6 and 15 outliers respectively was carried out. The results showed that the median adequacy measures performed well and described adequately the models variation in the dependent variable, predictive performance and efficiency without outliers and better when the data contain outliers for both the real data and simulated data models.