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Test Your Understanding 19

A MLR is fit to a set of data. The estimated standard error for the mean response a specified set of regressor values $x_{1},x_{2},\ldots, x_{q}$, is 12.96, while the estimated standard error of prediction of a future observation at the same set of regressor values is 19.46. What is the MSE from the model fit?

ANS: From the formula on p. 483 of the text,

$19.46=\sqrt{\mbox{MSE}+12.96^2}$, so that $\mbox{MSE}=19.46^2-12.96^2=210.73$.

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