I'm trying to show that $\hat{y} = X(X^TX)^{-1}X^Ty = \tilde{X}(\tilde{X}^T\tilde{X})^{-1}\tilde{X}^Ty$, where each column in $\tilde{X}$ is normalized by subtracting the mean and dividing by standard deviation. Is this even true?
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No it is not true – Russ Lenth Aug 05 '20 at 03:22
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See here: https://stats.stackexchange.com/questions/29781/when-conducting-multiple-regression-when-should-you-center-your-predictor-varia – kurtosis Aug 05 '20 at 03:26