<p>Regression analysis is extensively used in statistical research for estimation and prediction. To address the issues of multicollinearity and outliers in classical linear regression models, Liu and robust estimators were developed. This paper examines the impact of various robust weight functions within the Liu regression framework to enhance its performance and simultaneously address multicollinearity and outliers. The proposed Liu regression procedures based on the robust weight functions Tukey, Cauchy, Andrews and Welsch are applied to both real and simulated datasets. The performances of regression procedures such as Ordinary Least Squares, Ridge, M, Liu, MM_Liu, TukeyLiu, CauchyLiu, AndrewLiu, and WelschLiu regression are assessed using the Mean Squared Error criterion. The study finds that the WelschLiu procedure outperforms the other regression methods in datasets affected by both multicollinearity and outliers, yielding more reliable results. This approach is beneficial for researchers in machine learning, as it accommodates factors like multicollinearity, outliers, and high dimensionality. This new procedure represents a significant advancement in regression analysis, offering a robust solution for complex data challenges.</p>