91Ó°ÊÓ

$\begin{array}{|ccccc|}\hline x& 1& 3& 4& 4\\ y& 13& -1& 3& 5\\ \hline\end{array}$

$\hat{y}=14-3x$

Decide the Null and Alternate hypothesis

$H_0:{\mathrm{β}}_1=0$($x$is not useful for predicting $y$).

$H_{\mathrm{Î\pm }}:{\mathrm{β}}_1≠0$($x$is useful for predicting $y$).

If $p$-value $≤\mathrm{Î\pm }(=0.10)$, then reject the null hypothesis $\left(H_0\right)$.

Using Excel, find the test statistic and $p$-value.

Step 1: Select Data >Data Analysis > Regression from the drop-down menu.

Step 2: In the Input Y Range box, type $y$.

Step 3:In the Input X Range box, type $x$.

Step 4: Select Confidence Level$90$from the drop-down menu.

Step 5: Click the OK button.

OUTPUT

The test statistic's value is $-1.470$, and the $p$-value is $0.2794$, according to the Excel output.

Use the $\mathrm{Î\pm }=0.10$significance level.

The p-value is higher than the level of significance in this case.

To put it another way, $p$-value $(=0.2794)>\mathrm{Î\pm }(=0.10)$.

As a result of the rejection rule, it may be argued that at $\mathrm{Î\pm }=0.10$, there is no evidence to reject the null hypothesis ( $H_0$).

$\begin{array}{|ccccc|}\hline x& 1& 3& 4& 4\\ y& 13& -1& 3& 5\\ \hline\end{array}$

$\hat{y}=14-3x$

Using Excel, calculate the $90\%$confidence interval for the slope of the regression line.

From the Excel output in part (a) We get as $(-8.960,2.960)$