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Linear Transformations of the data, consider the least squares regression of y on K variables (with a constant) X. Consider an alternative set of regressors Z = XP, where P is a nonsingular matrix. Thus, each column of Z is a mixture of some of the columns of X. Prove that the residual vectors in the regressions of y on X and y on Z are identical. What relevance does this have to the question of changing the fit of a regression by changing the units of measurement of the independent variables? |
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