Çoklu Doğrusal Bağlantı Durumunda En Küçük Kareler ve Bazı Yanlı Tahmin Edicilerin Karşılaştırılması

Abstract

The aim of this study is to compare the least squares (LS) method that lost its function in the case of multicollinearity in regression methods with Ridge Regression (RR) and Principal Components Regression (PCR) which are bias estimators. For this aim, the effect of some body measurements on body weight (BW), body length (BL), height at withers (HW), height at rump (HR), chest depth (CD), chest girth (CG) and chest width (CW) obtained from 59 Saanen kids at weaning period raised at Research Farm of Tokat Gaziosmanpaşa University. Determination coefficient (R2) and mean square error (MSE) values were used to evaluate the estimation performance of the methods. The multicollinearity between height at withers (HW) and height at rump (HR) which were used to estimate body weight was eliminated by using RR and PCR. When R2 and HKO values of the examined methods are compared; It has been shown that RR method have better results of live weight of Saanen goats.

Use of ridge regression analysis in the multicollinearity in animal science

“…It was determined as 8 and the results are similar to the results of our study. The findings of our study were reported by Yılmaz et al (2020) in their study, using the 56th day data of wither height, body length, rump height and chest circumference measurements of the Saanen (59) kid raised at Tokat Gaziosmanpaşa University research and application farm, applying Ridge regression analysis by determining the multicollinearity problem and determining the smallest As a result of square regression analysis, the R 2 value was determined as 66.0% and as a result of the ridge regression analysis, the R 2 value was determined as 65.9%, which is compatible with the study findings. Tırınk et al (2020) compared the LS method used in multicollinearity determined by the VIF value with the ridge regression method to estimate body weight, and the RR method was based on some body measurements (spine length, rump height, body length, chest depth, The findings of our study are similar to the findings of our study, where the R 2 value was found to be 88.0% as a result of the least squares regression analysis and the R 2 value was found to be 87.6% as a result of the ridge regression analysis.…”

“…In the above equation; Y: n × 1 dimensional dependent variable vector, X: n × (p+1) dimensional independent variables matrix, β: (p+1) × 1 dimensional vector of coefficients, and ε: n × 1 dimensional error vector (Yılmaz et al, 2020).…”