The Solution of Multicollinearity Problem via Biased Regression Analysis in Southern Anatolian Red Cattle

Abstract

The aim of this study is to investigate the effectiveness of biased estimation methods, principal component regression (PC) and ridge regression (RR) methods, according to unbiased the least squares (LS) method, against the multiple linearity problem (multicollinearity) encountered in regression methods. For this purpose to fit a model on account to predict body weight from some body measurements of 32 South Anatolian Red Kilis (SAR) cattle of different ages. R2, RMSE, MSE, and CV were used as the goodness of fit criteria for the performance of the models. According to these criteria respectively, 0.9970, 0.0224, 0.0005, 0.0099 for LS; 0.9970, 0.0224, 0.0005, 0.0099 for PC; and 0.9876, 0.0455, 0.0021, 0.0201 of k=0.02 for RR gave the best fit values. According to these results, LR and PC showed the best fit. But RR and PC techniques from biased prediction techniques provided more consistent, valid, stable, and theoretical expectations than LS technique, since LR did not provide the necessary assumptions.

Keywords

• multicollinearity
• biased regression analysis
• ridge regression
• principal component regression
• least squares method
• south anatolian red kilis (sar) cattle