This paper presents a modification to ordinary least squares (OLS) method with a view to overcoming the ill-effects of collinearity on the OLS estimates of the regression parameters in a linear model with two explanatory variables. This modified approach leads to estimates that are, to a large extent, better than OLS estimates under the mean square error criterion and also overcome the overestimation problem that plagues the OLS estimates. Although a few attempts to get improved estimates have been made by some authors, the method developed here takes a route that has not been hitherto ventured in the context of addressing collinearity issues.
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