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(Solved) Show that an equivalent way to perform the test for significance of regression in multiple linear regression is to base the test on R^2 as follows:

Question: Show that an equivalent way to perform the test for significance of regression in multiple linear regression is to base the test on \(R^{2}\) as follows: To test \(H_{0}: \beta_{1}=\beta_{2}=\cdots=\beta_{k}\) versus \(H_{1}:\) at least one \(\beta_{j} \neq 0\), calculate

\[F_{0}=\frac{R^{2}(n-p)}{k\left(1-R^{2}\right)}\]

and to reject \(H_{0}\) if the computed value of \(F_{0}\) exceeds \(F_{\alpha, k, n-p}\), where \(p=k+1\)

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