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R-squared and s Answers

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1
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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. A regression analysis was completed and the value for s was found to be 3.05.

A
The average residual is about 3.05 pretzels.
B
The average residual is about 3.05 centimeters.
C
The average handspan of a student is 3.05 centimeters.
D
The average number of pretzels a student could grab is 3.05 pretzels.
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.

Question illustration
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

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. An analysis is performed on the data for 15 randomly selected students and is displayed in the computer output.Which of the following represents the value of the average residual for a student’s GPA?

Question illustration
A
–0.096
B
0.0393
C
0.3120
D
0.691
4

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.

Question illustration
A
The correlation will be weakened because the point has a large negative residual.
B
The correlation will be weakened because the point falls outside the pattern of the data.
C
The correlation will be strengthened because the point has a large negative residual.
D
The correlation will be strengthened because the point falls outside the pattern of the data.
5

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 represents the standard deviation of the residuals?

Question illustration
A
0.035
B
0.186
C
1.61
D
2.567
6

The length, x (in inches), and weight, y (in ounces), for a type of bass were measured for a random sample of 10 bass from a lake. These measurements were then analyzed and the value for r2 was determined to be 96%.

A
4% of the variation in the bass’s length is determined by the variation in the bass’s weight.
B
96% of the variation in the bass’s weight is determined by the variation in the bass’s length.
C
96% of the variation in the bass’s length is determined by the variation in the bass’s weight.
D
98% of the variation in the bass’s weight is determined by the variation in the bass’s length.
7

The owner of a used car dealership is trying to determine if there is a relationship between the price of a used car and the number of miles it has been driven. The owner collects data for 25 cars of the same model with different mileage and determines each car’s price using a used car website. The analysis is given in the computer output.Which of the following represents the value of the average residual for a car’s price?

Question illustration
A
0.024
B
2164.1
C
3860.7
D
24157.2
8

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?

Question illustration
A
0.63
B
0.65
C
0.79
D
0.81
9

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.
10

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 given data list the number of absences and GPAs for 15 randomly selected students.Using technology, what is the value of r2?

Question illustration
A
–0.56
B
–0.32
C
0. 32
D
0.56
11

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. A regression analysis was completed and the value for r2 was 52.1%.

A
About 52.1 percent of the variation in handspan is accounted for by the linear relationship formed with the number of bite-sized pretzels grabbed with the dominant hand.
B
About 52.1 percent of the variation in number of bite-sized pretzels grabbed with the dominant hand is accounted for by the linear relationship formed with handspan.
C
About 47.9 percent of the variation in handspan is accounted for by the linear relationship formed with the number of bite-sized pretzels grabbed with the dominant hand.
D
About 72.1 percent of the variation in number of bite-sized pretzels grabbed with the dominant hand is accounted for by the linear relationship formed with handspan.
12

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)

Question illustration
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.

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