Chapter 11.1, Problem 25E

a.

To determine

To interpret: The y-intercept in the context of provided study.

Explanation of Solution

Given:

The figure is:

  

The regression line is given as:

  $GPA=3.42+0.0243\left(\text{Books Read}\right)$

Here, y-intercept is 3.42 which means that if no book is read by any of the students then the English grades are expected to be approx. 3.42.

b.

To determine

To find: The residual of the student.

Answer to Problem 25E

The confidence interval is (0.11968, 0.44832)

Explanation of Solution

Given:

Number of books read = 17

GPA = 2.85

Calculation:

The estimated GPA could be calculated as:

  $\begin{array}{c}\widehat{GPA}=3.42+0.0243\left(17\right)\\ =3.8331\end{array}$

Now the residual is computed as:

  $\begin{array}{c}\text{Residual=}\widehat{GPA}-GPA\\ =2.85-3.8331\\ =-0.9831\end{array}$

Thus, the required residual is -0.9831.

c.

To determine

To explain: The extent of the relationship between the two variables.

Answer to Problem 25E

There is a weak relationship between the variables.

Explanation of Solution

The coefficient of determination shows the variation that is explained by the predictor variable on the response variable. Here, coefficient of determination is 0.083.

Since, the coefficient of determination is low. Thus, it could be said that there is a weak relationship between the variables.