We address the estimation of regression parameters for the ill-conditioned predictive linear model in this study. Traditional least squares methods often encounter challenges in yielding reliable results when there is multicollinearity. Therefore, we employ a better shrinkage method, average least squares-centered penalized regression (ALPR), as it offers a more efficient approach for handling multicollinearity than ridge regression. Additionally, we integrate ALPR with the principal component (PC) dimension reduction method for enhanced performance. We compared the proposed PCALPR estimation technique with existing ones for ill-conditioned problems through comprehensive simulations and real-life data analyses using the mean squared error. This integration results in superior model performance compared to other methods, highlighting the potential of combining dimensionality reduction techniques with penalized regression for enhanced model predictions.

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