A group-based approach to the least squares regression for handling multicollinearity from strongly correlated variables
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Multicollinearity due to strongly correlated predictor variables is a long-standing problem in regression analysis. It leads to difficulties in parameter estimation, inference, variable selection and prediction for the least squares regression. To deal with these difficulties, we propose a group-based approach to the least squares regression centered on the collective impact of the strongly correlated variables. We discuss group effects of such variables that represent their collective impact, and present the group-based approach through real and simulated data examples. We also give a condition more precise than what is available in the literature under which predictions by the least squares estimated model are accurate. This approach is a natural way of working with multicollinearity which resolves the difficulties without altering the least squares method. It has several advantages over alternative methods such as ridge regression and principal component regression.
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