Question

In a simple regression analysis for a given data set, if the null hypothesis β = 0 is rejected, then the null hypothesis ρ = 0 is also rejected. This statement is ___________ true. always

Answer 1

Answer:

Null hypothesis: $\rho =0$

Alternative hypothesis: $\rho \neq 0$

The statistic to check the hypothesis is given by:

$t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}$

And is distributed with n-2 degrees of freedom

And the statistic to check the significance of a coeffcient in a regression is given by:

$t_1 = \frac{\hat{\beta_1} -0}{S.E (\hat{\beta_1})}$

For this case is importantto remember that t1 and p value for test of slope coefficient is the same test statistic and p value for the correlation test so then the answer would be:

Always

Step-by-step explanation:

In order to test the hypothesis if the correlation coefficient it's significant we have the following hypothesis:

Null hypothesis: $\rho =0$

Alternative hypothesis: $\rho \neq 0$

The statistic to check the hypothesis is given by:

$t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}$

And is distributed with n-2 degrees of freedom

And the statistic to check the significance of a coeffcient in a regression is given by:

$t_1 = \frac{\hat{\beta_1} -0}{S.E (\hat{\beta_1})}$

For this case is importantto remember that t1 and p value for test of slope coefficient is the same test statistic and p value for the correlation test so then the answer would be:

Always