Question

In Chapter $3$, we examined data on the body weights and backpack weights of a group of eight randomly selected ninth-grade students at the Webb Schools. Some Minitab output from least-squares regression analysis for these data is shown.

2. With such a small sample size, it is difficult to check several of the conditions for regression inference. Assume that the conditions are met. Construct and interpret a $95\%$confidence interval for the slope of the population regression line.

Short answer

True regression line is between$(0.021525,0.160075)$.

Step-by-step solution

Given Information

It is given in the Question that:

Explanation

The sample size was reduced by $2$degrees of freedom.

$$\begin{gathered} df=n-2 \\ =8-2 \\ =6 \end{gathered}$$

In table B, the critical t-value can be discovered in the row of $df=6$and the column of $c=95\%$as follows:

$t^{\ast }=2.447$

The confidence interval is will be,

localid="1652249759789" $$\begin{gathered} b-t^{*}\times {\mathrm{SE}}_b=0.09080-2.447\times 0.02831 \\ =0.021525 \end{gathered}$$

$$\begin{gathered} b+t^{\ast }\times {\mathrm{SE}}_b=0.09080+2.447\times 0.02831 \\ =0.160075 \end{gathered}$$

Therefore the true regression line lies between $(0.021525,0.160075)$in $95\%$confidence interval.