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R-squared and s Answers

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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
2
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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.
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. 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.
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. 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.
5

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 computer output displays the regression analysis.Which of the following represents the typical distance between the actual and predicted numbers of pretzels?

Question illustration
A
0.310
B
3.05
C
4.317
D
5.114
6

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 computer output displays the regression analysis.Using the computer output, what is the value of r2?

Question illustration
A
0.521
B
0.547
C
1.585
D
3.05
7

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
8

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.
9

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.
10

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

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