Consider the simple linear regression model based on
Chapter 11, Problem 55E(choose chapter or problem)
Consider the simple linear regression model based on normal theory. If we are interested in testing \(H_{a}: \beta_{1}=0\) versus various alternatives, the statistic
\(T=\frac{\tilde{\beta_{1}}=0}{S / \sqrt{S_{x x}}}\)
possesses a t distribution with n − 2 df if the null hypothesis is true. Show that the equation for T can also be written as
\(T=\frac{r \sqrt{n-2}}{\sqrt{1-\gamma^{2}}}\)
Equation transcription:
Text transcription:
H_{a}: \beta_{1}=0
T=frac{tilde{beta{1}}=0}{S / sqrt{S{x x}}}
T=frac{r sqrt{n-2}}{sqrt{1-gamma^{2}}}
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