Chapter 11.1, Problem 26E

a)

To determine

To interpret slope and y-intercept.

Answer to Problem 26E

The y-intercept explain the average grade is 3.42 when 0 books read.

The slope explains the average English grade increases by 0.02 per book read.

Explanation of Solution

Given:

The box plot:

Scatter plot:

The least square regression line is,

  $\widehat{y}=3.42+0.02x$

Calculation:

The y-intercept is 3.42 which explain the average grade is 3.42 when 0 books read.

The slope is 0.02 which explain the average English grade increases by 0.02 per book read.

b)

To determine

To calculate residuals.

Answer to Problem 26E

We overestimated the average grade by 0.9831 when making the prediction using the lease square regression equation.

Explanation of Solution

Given:

The box plot:

Scatter plot:

The least square regression line is,

13 $\widehat{y}=3.42+0.02x$

GPA for English = y =2.85

Formula:

  $\mathrm{Re}sidual=y-\widehat{y}$

Calculation:

First, we need to put value of $x=17$ to calculate predicted value.

  $\widehat{y}=3.42+0.02\times 17=3.8331$

Therefore, residual is,

  $\mathrm{Re}sidual=2.85-3.8331=-0.9831$

This can be interpreted as, we overestimated the average grade by 0.9831 when making the prediction using the lease square regression equation.

c)

To determine

To interpret value of r²

Answer to Problem 26E

The 8.3% of the variation in the average English grade is explained by the model using the number of books read.

Explanation of Solution

Given:

The box plot:

Scatter plot:

r² = 0.083

Calculation:

The r² = 0.083 = 8.3%. This value is very small. Therefore, 8.3% of the variation in the average English grade is explained by the model using the number of books read.