Chapter 7.1, Problem 26E

a.

To determine

To find: The equation of the least square regression line.

Answer to Problem 26E

The equation of the regression line is $\widehat{y}=1.4146+0.4399x$

Explanation of Solution

Given:

The output is:

  

The general equation of the regression line is written as:

  $\begin{array}{l}\widehat{y}=a+bx\\ a\text{ is the y-intercept}\\ b\text{ is the slope coefficient}\end{array}$

Using the provided information, the general equation of the regression line could be written as:

  $\begin{array}{l}\widehat{y}=a+bx\\ \widehat{y}=1.4146+0.4399x\end{array}$

Thus, the equation of the regression line is $\widehat{y}=1.4146+0.4399x$

b.

To determine

To explain: The linearity of the model using the residual plot.

Explanation of Solution

In the residual plot, no pattern could be seen and it is centered around the 0 which implies that it is a good linear model.

c.

To determine

To explain: The $r^2\text{ and }s$ .

Explanation of Solution

Here, $r^2$ is 57.2% and it implies that 57.2% of the variation are being described by the regression model.

The value of s shows that the average number of errors being made are 0.6000309.