Weighted regression analysis for comparing varietal adaptation.

Area of Science:

• Agricultural Science
• Biometrics
• Genetics

Background:

• Ordinary Least Squares (OLS) regression is commonly used for analyzing genotype-environment interactions and estimating stability parameters.
• Heterogeneous error variances across testing sites can compromise the accuracy of OLS estimates for stability parameters.
• Accurate estimation of stability parameters is crucial for selecting superior crop varieties with predictable performance.

Purpose of the Study:

• To compare the precision of Weighted Regression Analysis (WLS) against Ordinary Least Squares (OLS) for estimating stability parameters in crop varieties.
• To evaluate the impact of heterogeneous site error variances on the estimation of regression coefficients (bᵢ).
• To assess differences in variety classification for general and specific adaptation between WLS and OLS methods.

Main Methods:

• Employed joint linear regression analysis (OLS) and Weighted Regression Analysis (WLS).
• Utilized grain yield data (kg ha⁻¹) from pearl millet [Pennisetum typhoides (Burm.) S. & H.] varieties and a hybrid.
• Data comprised 12 varieties and one hybrid tested across 26 diverse sites in India.

Main Results:

• Weighted regression analysis (WLS) provided more precise estimates of stability parameters compared to OLS when site error variances were heterogeneous.
• WLS yielded more efficient regression coefficients (bᵢ), with standard errors reduced by up to 43% compared to OLS.
• Significant differences were observed in the estimated bᵢ values and the classification of varieties based on adaptation (general vs. specific) between the two analytical methods. Five varieties showed significant deviation from unity with WLS, versus only one with OLS.

Conclusions:

• Weighted regression analysis (WLS) is a more appropriate and accurate method than OLS for comparing stability parameters of crop varieties under heterogeneous site error variances.
• WLS enhances the reliability of regression coefficient estimates and improves the accuracy of classifying varieties based on their adaptive responses.
• The choice of analytical method significantly impacts the interpretation of variety performance and adaptation, highlighting the importance of considering error variance structures in biometric analyses.