We have fit a model with k independent variables, and wish

Chapter 11, Problem 84E

(choose chapter or problem)

We have fit a model with k independent variables, and wish to test the null hypothesis $H_{0}: \beta_{1}=\beta_{2}=\ldots=\beta_{k}=0$

a Show that the appropriate F-distributed test statistic can be expressed as

$F=\frac{n(k+1)}{k}\left(\frac{R^{2}}{1-R^{2}}\right)$,

b If k = 1 how does the value of F from part (a) compare to the expression for the T statistic derived in Exercise 11.55?

Equation transcription:

${H}_{0}:{\beta{}}_{1}={\beta{}}_{2}=...={\beta{}}_{k}=0$

$F=\frac{n(k+1)}{k}(\frac{{R}^{2}}{1-{R}^{2}})$

Text transcription:

H_{0}: beta{1}=beta{2}=ldots=beta{k}=0

F={n(k+1)}{k}({R^{2}}{1-R^{2}})

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