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Chapter 11: Q.25 (page 695)

Reading and grades (3.2) The Fathom scatterplot below show the number of books read and the English grade for all 79students in the study. A least-squares regression line has been added to the graph.

(a) Interpret the meaning of the y-intercept in context.

(b) The student who reported reading 17books for pleasure had an English GPA of 2.85. Find this student’s residual. Show your work.

(c) How strong is the relationship between English grades and the number of books read? Give appropriate evidence to support your answer.

Short Answer

Expert verified

a).y-intercept is3.42.

b). The confidence interval is (0.11968,0.44832).

c). There is a weak relationship between the variables.

Step by step solution

01

Part (a) Step 1: Given Information

The figure is,

02

Part (a) Step 2: Explanation

The regression line is given as:

GPA=3.42+0.0243(Books Read)

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.

03

Part (b) Step 1: Given Information

Number of books read =17.

GPA=2.85.

04

Part (b) Step 2: Explanation

The estimated GPA could be calculated as:

GPA=3.42+0.0243(17)=3.8331

Now the residual is computed as:

Residual=GPA^-GPA=2.85-3.8331=-0.9831

Thus, the required residual is -0.9831.

05

Part (c) Step 1: Given Information

06

Part (c) Step 2: Explanation

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

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