Question

6. In simple regression to test the hypothesis of H0: \(\beta_1 = 0\) versus HA: \(\beta_1 \neq 0\) T distribution with n-2 degrees of freedom is used. Show that test statistic under H0 is \(T = \frac{r\sqrt{n-2}}{\sqrt{1-r^2}}\), where r is sample correlation coefficient.

          6. In simple regression to test the hypothesis of H<sub>0</sub>: \(\beta_1 = 0\) versus H<sub>A</sub>: \(\beta_1 \neq 0\)

T distribution with n-2 degrees of freedom is used. Show that test statistic under H<sub>0</sub> is

\(T = \frac{r\sqrt{n-2}}{\sqrt{1-r^2}}\),

where r is sample correlation coefficient.

6. In simple regression to test the hypothesis of H<sub>0</sub>: β1 = 0 versus H<sub>A</sub>: β1 ≠ 0

T distribution with n-2 degrees of freedom is used. Show that test statistic under H<sub>0</sub> is

T = (r√(n-2))/(√(1-r^2)),

where r is sample correlation coefficient.

Added by Claudia K.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Victor Salazar

10/29/2022

Step 1

The test statistic in simple regression is given by: t = r * √((n-2) / (1 - r^2)) where: - t is the test statistic - r is the correlation coefficient between the independent variable and the dependent variable - n is the sample size Show more…

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6. In simple regression to test the hypothesis of Ho: β = 0 versus Hi: β ≠ 0, a T distribution with n-2 degrees of freedom is used. Show that the test statistic under Ho is: t = r * √((n-2) / (1 - r^2))