Chapter 12.1, Problem 12E

To determine

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

Answer to Problem 12E

There are 95% confident that the slope of the true regression line is between 0.0452898 and 0.0963102

Explanation of Solution

Given:

  

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

  

  

  

  $\begin{array}{l}n\text{=24}\\ c\text{ = Confidence level =95\% =0}\text{.95}\end{array}$

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 “Mentos” and in the column “coef” of the mention computer output:

  $b_1=0.0708$

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

  $S{E}_{b_1}=0.0123$

The critical value could be found in the T distribution table $df-n-2=24-2=22$ and in the column of $c\text{ = 95\%}$ :

  $t^{\ast }=2.074$

The boundaries of the confidence interval

  $\begin{array}{l}b-t^{\ast }\times S{E}_b=0.0708-2.074\times 0.0123=0.0452898\\ b+t^{\ast }\times S{E}_b=0.0708+2.074\times 0.0123=0.0963102\end{array}$

There are 95% confident that the slope of the true regression line is between 0.0452898 and 0.0963102