Chapter 12.1, Problem 11E

To determine

To construct: and interpret the 95% confidence interval for the slope of the true regression line.

Answer to Problem 11E

There are 95% confident that the slope of the regression line is between -2.9962298 and -2.2737702.

Explanation of Solution

Given:

  

Computer output from the least squares regression analysis of the given data.

  

  

  

  

  $\begin{array}{l}n=\text{40}\\ c\text{ = Confidence level =95\% =0}\text{.95}\end{array}$

Formula used:

The boundaries of the confidence interval

  $\begin{array}{l}b-t^{\ast }\times S{E}_b\\ b+t^{\ast }\times S{E}_b\end{array}$

Calculation:

The calculation of the slope $b_1$ is mention in the row “Tapping time” and in the column “coef” of the mention computer output:

  $b_1=-2.6350$

The calculated standard deviation of the slope $S{E}_{b_1}$ is mention in the row “tapping time” and in the column “SE Coef” of the given computer output:

  $S{E}_{b_1}=0.1769$

The critical can be found in the T distribution table $df-n-2=40-2=38$

  $df=38$ , therefore it would utilize the closest smaller degrees of freedom $df=30$ instead and in the column of $c\text{ = 95\%}$ :

  $t^{\ast }=2.042$

The boundaries of the confidence interval

  $\begin{array}{l}b-t^{\ast }\times S{E}_b=-2.6350-2.042\times 0.1769=-2.9962298\\ b+t^{\ast }\times S{E}_b=-2.6350+2.042\times 0.1769=-2.2737702\end{array}$

There are 95% confident that the slope of the regression line is between -2.9962298 and -2.2737702.