AnswersStatistics and ProbabilitySimple Linear Regression

Simple Linear Regression — Test Answers

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The equation of the least-squares regression line is hat y is equal to 68 point 5 plus 11 point 4 x , where hat y is the number of students enrolled and x is number of years the school has been open. Which shows the residual plot?

A
Image with description A dot plot with the x axis titled Number of years begins with 0 and ends at 8 with equal intervals of 2, such as 0, 2, 4, 6, and 8. The y axis titled Residual begins with negative 80 and ends at 20 with equal intervals of 20, such as negative 80, negative 60, negative 40, negative 20, 0, and 20. A horizontal line parallel to the x axis starts from the point where y is 0. There is 1 dot at approximately 1, 18; 1 dot at 2, 16; 1 dot at 3, 10; 1 dot at 4, 5; 1 dot at 5, negative 2; 1 dot at 6, negative 22, 1 dot at 7, negative 39; and 1 dot at 8, negative 70.
B
Image with description A dot plot with the x axis titled Number of years begins with 0 and ends at 8 with equal intervals of 2, such as 0, 2, 4, 6, and 8. The y axis titled Residual begins with negative 15 and ends at 20 with equal intervals of 5, such as negative 15, negative 10, negative 5, 0, 5, 10, 15, and 20. A horizontal line parallel to the x axis starts from the point where y is 0. There is 1 dot at approximately 1, 12; 1 dot at 2, 3; 1 dot at 3, negative 3; 1 dot at 4, negative 10; 1 dot at 5,negative 12; 1 dot at 6, negative 6, 1 dot at 7, negative 1; and 1 dot at 8, 16.
C
Image with description A dot plot with the x axis titled Number of years begins with 0 and ends at 8 with equal intervals of 2, such as 0, 2, 4, 6, and 8. The y axis titled Residual begins with negative 20 and ends at 15 with equal intervals of 5, such as negative 20, negative 15, negative 10, negative 5, 0, 5, 10, and 15. A horizontal line parallel to the x axis starts from the point where y is 0. There is 1 dot at approximately 1, negative 12; 1 dot at 2, negative 3; 1 dot at 3, 3; 1 dot at 4, 10; 1 dot at 5, 12; 1 dot at 6, 6, 1 dot at 7, 1; and 1 dot at 8, -16.
D
Image with description A dot plot with the x axis titled Number of years begins with 0 and ends at 8 with equal intervals of 2, such as 0, 2, 4, 6, and 8. The y axis titled Residual begins with negative 20 and ends at 80 with equal intervals of 20, such as negative 20, 0, 20, 40, 60, and 80. A horizontal line parallel to the x axis starts from the point where y is 0. There is 1 dot at approximately 1, negative 18; 1 dot at 2, negative 16; 1 dot at 3, negative 10; 1 dot at 4, negative 5; 1 dot at 5, 5; 1 dot at 6, 22, 1 dot at 7, 38, and 1 dot at 8, 75.
2
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Which is a true statement regarding Springside?

A
Removing Springside would increase the value of the correlation coefficient.
B
Springside strengthens the correlation shown in the scatterplot.
C
Springside weakens the correlation shown in the scatterplot.
D
Springside does not affect the correlation.
3

Which statement regarding the association shown could explain the relationship?

A
Schools in more affluent areas have smaller class sizes, which is associated with higher test scores.
B
Schools in more affluent areas have larger class sizes, which is associated with higher test scores.
C
Schools in less affluent areas tend to have smaller class sizes, which is associated with lower test scores.
D
Class size appears to have little effect on test scores.
4

Using the computer output, what is the correlation?

A
0 point 7 9 4
B
0 point 6 4 9
C
0 point 6 3 0
D
0 point 8 0 6
5

What effect does the circled point have on the slope and y - intercept of the least-squares regression line?

A
This point will decrease the value of the slope and decrease the value of the y - intercept.
B
This point will increase the value of the slope and increase the value of the y - intercept.
C
This point will decrease the value of the slope and increase the value of the y - intercept.
D
This point will increase the value of the slope and decrease the value of the y - intercept.
6

Using the computer output, what is the predicted foot length for a student with an arm span of 160 cm?

A
5 point 7 9 cm
B
22 point 1 5 cm
C
29 point 8 0 cm
D
29 point 7 6 cm
7

Which scatterplot represents the student data?

A
Image with description A scatter plot titled high school and college G P A has College G P A on the x-axis, and H S G P A on the y-axis. Points are at (2.8, 2.5), (2.9, 2.25), (2.9, 3.5), (3, 2.5), (3, 3), (3, 3.25), (3, 3.5), (3, 4), (3.1, 3.5), (3.1, 4), (3.2, 3.25).
B
Image with description A scatter plot titled high school and college G P A has H S G P A on the x-axis, and College G P A on the y-axis. Points are at (3.25, 3.2), (3.5, 3.0), (3.5, 2.9), (3.25), (3.0), (2.5, 3.0), (4, 3.0), (4, 3.1), (3.5, 3.1), (3.25, 3.1), (3.25, 3.1), (3.5, 3.0), (3.5, 3.0), (4, 3.1), (3, 3.0), (3.5, 3.1), (2.25, 2.9), (2.5, 2.8).
C
Image with description A scatter plot titled high school and college G P A has H S G P A on the x-axis, and College G P A on the y-axis. Points are at (3.25, 3.2), (3.5, 3.0), (3.5, 2.9), (3.25), (3.0), (2.5, 3.0), (4, 3.0), (4, 3.1), (3.5, 3.1), (3.25, 3.1), (3.25, 3.1), (3.5, 3.0), (3.5, 3.0), (4, 3.1), (3, 3.0), (3.5, 3.1), (2.25, 2.9), (2.5, 2.8), (4, 3.2).
D
Image with description A scatter plot titled high school and college G P A has College G P A on the x-axis, and H S G P A on the y-axis. Points are at (2.8, 2.5), (2.9, 2.25), (2.9, 3.5), (3, 2.5), (3, 3), (3, 3.25), (3, 3.5), (3, 4), (3.1, 3.25), (3.1, 3.5), (3.1, 4), (3.2, 3.25).
8

Which of the following is an accurate description of the scatterplot?

A
The more seeds that are planted per square foot, the larger the expected yield of the crop.
B
The more seeds that are planted per square foot, the smaller the expected yield of the crop.
C
The expected yield of a crop is low whenever the number of seeds planted per square foot is small or large. A larger yield is expected when the number of seeds per square foot is around 60.
D
The expected yield of a crop is high whenever the number of seeds planted per square foot is small or large. A larger yield is expected when the number of seeds per square foot is around 60.
9

Using technology, what is the slope of the least-squares regression line and what is its interpretation?

A
The slope is 1 point 9 8 , which means for each additional inch in height, the child’s weight will increase by 1 point 9 8 pounds.
B
The slope is 0 point 5 0 , which means for each additional pound in weight, the child’s height is predicted to increase by 0 point 5 inches.
C
The slope is 0 point 5 0 , which means for each additional pound in weight, the child’s height will increase by 0 point 5 inches.
D
The slope is 1 point 9 8 , which means for each additional inch in height, the child’s weight is predicted to increase by 1 point 9 8 pounds.
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. Open image in full-screen view Which of the following is the best interpretation of the coefficient of determination r squared ?

A
About 63 percent of the variation in foot length is accounted for by the linear relationship formed with the arm span.
B
About 63 percent of the variation in arm span is accounted for by the linear relationship formed with the foot length.
C
About 37 percent of the variation in arm span is accounted for by the linear relationship formed with the foot length.
D
About 65 percent of the variation in foot length is accounted for by the linear relationship formed with the arm span.
11

A nutritionist collects data from 25 popular breakfast cereals. For each cereal, the number of calories per serving is plotted on the x - axis against the number of milligrams of sodium on the y - axis. The value of r for the resulting scatterplot is 0 point 8 3 How would the value of the correlation coefficient, r , change if sodium was plotted on the x - axis and calories plotted on the y - axis?

A
The value of r would change to negative 0 point 8 3 .
B
The value of r would increase.
C
The value of r would not change.
D
The value of r could increase or decrease, depending of the strength of the new relationship.
12

A sports statistician was interested in the relationship between game attendance (in thousands) and the number of wins for baseball teams. Information was collected on several teams and was used to obtain the regression equation ŷ=4.9⁢x+15.2 , where x represents the attendance (in thousands) and widehat y is the predicted number of wins. What is the predicted number of wins for a team that has an attendance of 2 comma 100 ?

A
10 comma 305 point 2 wins
B
36 point 8 2 wins
C
25 point 4 9 wins
D
31 point 9 2 wins
13

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. Open image in full-screen view Using the computer output, what is the value of the coefficient of determination?

A
0 point 8 2
B
0 point 7 0
C
0 point 4 6
D
0 point 6 8
14

A sports statistician was interested in the relationship between game attendance (in thousands) and the number of wins for baseball teams. Information was collected on several teams and was used to obtain the regression equation widehat y is equal to 4 point 9 x plus 15 point 2 , where x represents attendance (in thousands) and widehat y is the predicted number of wins. Which statement best describes the meaning of the slope of the regression line?

A
For each increase in the number of wins by 1 , the predicted attendance increases by 4 comma 900 .
B
For each increase in attendance by 1 comma 000 , the predicted number of wins increases by 4 point 9 .
C
For each increase in attendance by 1 comma 000 , the predicted number of wins increases by 15 point 2 .
D
For each increase in the number of wins by 1 , the predicted attendance increases by 15 comma 200 .
15

Market researchers were interested in the relationship between the number of pieces in a building-brick set and the cost of the set. The researchers collected information from a survey and used it to obtain the regression equation widehat y is equal to 0 point 0 8 x plus 1 point 2 0 , where x represents the number of pieces in a set and widehat y is the predicted price (in dollars) of the set. What is the predicted price of a set that has 2 comma 520 pieces?

A
2 dollars comma 017 point 2 0
B
31 dollars comma 485
C
3 dollars comma 024 point 0 8
D
202 point 8 0 dollars
16

A certain standardized test measures students’ knowledge in English and math. The English and math scores for 10 randomly selected students were recorded and analyzed. The results are shown in the computer output. Open image in full-screen view Which of the following represents the standard deviation of the residuals?

A
124 point 1 3
B
1 point 2 2 3
C
78 point 7 1 2
D
34 point 5 5
17

College administrators at a small, private college noticed that students who had higher high school GPAs tend to have higher college GPAs. What are the explanatory variable and response variable for this relationship?

A
Explanatory variable: college GPA Response variable: high school GPA
B
Explanatory variable: type of college (private vs. public) Response variable: college GPA
C
Explanatory variable: size of college Response variable: college GPA
D
Explanatory variable: high school GPA Response variable: college GPA
18

A sports analyst determines that the number of points scored in a basketball game is related to the number of shots taken during the game. The least-squares regression line is hat y is equal to 5 point 0 plus 1 point 2 x , where start set hat y end set is the predicted number of points scored and x is the number of shots taken. In one game, a team takes 50 shots and the residual is negative 10 How many points were scored by this team in this game?

A
55
B
45
C
65
D
75
19

Based on data taken from airline fares and distances flown, it is determined that the equation of the least-squares regression line is hat y is equal to 102 point 5 0 plus 0 point 6 5 x , where start set hat y end set is the predicted fare and x is the distance, in miles. One of the flights was 350 miles and its residual was negative 105 point 0 0 What was the fare for this flight?

A
435 point 0 0 dollars
B
330 point 0 0 dollars
C
102 point 5 0 dollars
D
225 point 0 0 dollars
20

Market researchers were interested in the relationship between the number of pieces in a brick-building set and the cost of a set. Information was collected from a survey and was used to obtain the regression equation widehat y is equal to 0 point 0 8 x plus 1 point 2 0 , where x represents the number of pieces in a set and widehat y is the predicted price (in dollars) of a set. Which statement best describes the meaning of the y - intercept of the regression line?

A
When the price of a set is 0 dollars , the predicted number of pieces is 0 .
B
When the price of a set is 0 dollars , the predicted number of pieces is 1 point 2 0 .
C
When the number of pieces is 0 , the predicted price is 0 point 0 8 dollars . This interpretation is not meaningful because a set cannot have 0 pieces.
D
When the number of pieces is 0 , the predicted price is 1 point 2 0 dollars . This interpretation is not meaningful because a set cannot have 0 pieces.

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