R-squared and s Answers

In a statistics class, a teacher had the students complete an activity in which they grabbed as many bite-sized pretzels as they could with their dominant hand, without crushing them. The teacher then measured their handspan in centimeters. The scatterplot displays the data the teacher collected along with the least-squares regression line. One student with a handspan of 23 cm grabbed 38 pretzels (this point is circled on the graph)

A

This point will increase the value of the standard deviation of the residuals because it has a large positive residual.

B

This point will increase the value of the standard deviation of the residuals because it has a large negative residual.

C

This point will not affect the value of the standard deviation of the residuals because it has a large positive residual.

D

This point will decrease the value of the standard deviation of the residuals because it has a large negative residual.

2

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A guidance counselor wants to determine if there is a relationship between a student’s number of absences, x, and their grade point average (GPA), y. The data that were collected are displayed in the scatterplot and the least-squares regression line was calculated. One student with 2 absences has a GPA of 1.8. This point is circled on the graph.

A

The value of r2 would not be affected because the residual is negative.

B

The value of r2 would not be affected because this point follows the pattern of the data.

C

The value of r2 would increase substantially because this point does not follow the pattern of the data.

D

The value of r2 would decrease substantially because this point does not follow the pattern of the data.

3

The arm span and foot length were both measured (in centimeters) for each of 20 students in a biology class. The computer output displays the regression analysis.Which of the following is the coefficient of determination?

A

0.63

B

0.65

C

0.79

D

0.81

4

In a statistics class, a teacher had the students complete an activity in which they grabbed as many bite-sized pretzels as they could with their dominant hand, without crushing them. The teacher then measured their handspan in centimeters. The scatterplot displays the data the teacher collected along with the least-squares regression line. One student with a handspan of 23 cm grabbed 38 pretzels. This point is circled on the graph.

A

It will increase the value of the slope because its residual is a large positive value.

B

It will decrease the value of the slope because its residual is a large positive value.

C

It will increase the value of the slope because its residual is a large negative value.

D

It will decrease the value of the slope because its residual is a large negative value.

5

A guidance counselor wants to determine if there is a relationship between a student’s number of absences, x, and their grade point average (GPA), y. He collects data for 15 randomly selected students and determines the value for r2 was 31%.

A

31% of the variation in the number of absences is accounted for by the linear relationship with GPA.

B

69% of the variation in the number of absences is accounted for by the linear relationship with GPA.

C

31% of the variation in the GPA is accounted for by the linear relationship with number of absences.

D

56% of the variation in the GPA is accounted for by the linear relationship with number of absences.

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