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Residuals — Quiz Answers

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1
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The equation of the least-squares regression line is hat y is equal to 13 point 0 minus 0 point 2 5 9 x , where hat y is the depth of the water and x is the number of hours past midnight. Which shows the residual plot?

A
Image with description A dot plot with the x axis titled Number of Hours after Midnight begins with 0 and ends at 24 with equal intervals of 2, such as 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, and 24. The y axis titled Residual begins with negative 2 point 0 and ends at 1 point 6 with equal intervals of 0 point 4, such as negative 2, negative 1 point 6, negative 1 point 4, negative 1 point 2, negative 0 point 8, negative 0 point 4, 0, 0 point 4, 0 point 8, 1 point 2, and 1 point 6. A horizontal line parallel to the x axis starts from the point where y is 0. There is a dot at approximately 0, 0 point 5; a dot at 3, negative 0 point 8; a dot at 6, negative 1; a dot at 9, 0 point 4; a dot at 12, 0 point 6; a dot at 15, 1 point 4; a dot at 18, 1 point 3; a dot at 21, 0 point 2; and a dot at 24, negative 1 point 8.
B
Image with description A dot plot with the x axis titled Number of Hours after Midnight begins with 0 and ends at 24 with equal intervals of 2, such as 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, and 24. The y axis titled Residual begins with negative 4 and ends at 4 with equal intervals of 1, such as negative 4, negative 3, negative 2, negative 1, 0, 1, 2, 3, and 4. A horizontal line parallel to the x axis starts from the point where y is 0. There is a dot at approximately 0, 2 point 5; a dot at 3, 2 point 9; a dot at 6, 2 point 2; a dot at 9, 0 point 8; a dot at 12, negative 0 point 9, a dot at 15, negative 2 point 5; a dot at 18, negative 3 point 2; a dot at 21, negative 2 point 8; and a dot at 24, negative 1 point 5.
C
Image with description A dot plot with the x axis titled Number of Hours after Midnight begins with 0 and ends at 24 with equal intervals of 2, such as 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, and 24. The y axis titled Residual begins with negative 4 and ends at 4 with equal intervals of 1, such as negative 4, negative 3, negative 2, negative 1, 0, 1, 2, 3, and 4. A horizontal line parallel to the x axis starts from the point where y is 0. There is a dot at approximately 0, negative 2 point 5; a dot at 3, negative 2 point 9; a dot at 6, negative 2 point 2; a dot at 9, negative 0 point 8; a dot at 9, negative 0 point 9; a dot at 15, 2 point 5; a dot at 18, 3 point 2; a dot at 21, 2 point 8; and a dot at 24, 2 point 5.
D
Image with description A dot plot with the x axis titled Number of Hours after Midnight begins with 0 and ends at 24 with equal intervals of 2, such as 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, and 24. The y axis titled Residual begins with negative 1 point 6 and ends at 2 point 0 with equal intervals of 0 point 4, such as negative 1 point 5, negative 1 point 2, negative 0 point 8, negative 0 point 4, 0, 0 point 4, 0 point 8, 1 point 2, 1 point 6, and 2 point 0. A horizontal line parallel to the x axis starts from the point where y is 0. There is a dot at approximately 0, negative 0 point 5; a dot at 3, 0 point 8; a dot at 6, 1; a dot at 9, negative 0 point 4; a dot at 12, negative 0 point 6; a dot at 15, negative 1 point 4; a dot at 18, negative 1 point 3; a dot at 21, negative 0 point 2; and a dot at 24, 1 point 8.
2
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The equation of the least-squares regression line is hat y is equal to negative 146 point 7 plus 4 point 7 6 x , where hat y is the weight and x is the height. Which show the residual plot?

A
Image with description A dot plot with the x axis titled Height in Inches begins with 64 and ends at 78 with equal intervals of 4, such as 64, 66, 68, 70, 72, 76,and 78. The y axis titled Residual begins with negative 20 and ends at 20 with equal intervals of 5, such as negative 20, 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 a dot at approximately 65, 2; a dot at 66, 7; a dot at 67, negative 3; a dot at 68, 8; a dot at 69, negative 18; a dot at 69, 7; a dot at 70, 2; a dot at 71, negative 14; a dot at 74, 10; and a dot at 76, 15.
B
Image with description A dot plot with the x axis titled Height in Inches begins with 64 and ends at 78 with equal intervals of 4, such as 64, 66, 68, 70, 72, 76,and 78. The y axis titled Residual begins with negative 20 and ends at 40 with equal intervals of 10, such as negative 20, negative 10, 0, 10, 20, 30, and 40. A horizontal line parallel to the x axis starts from the point where y is 0. There is a dot at approximately 65, negative 15; a dot at 66, negative 15; a dot at 67, 0; a dot at 68, negative 5; a dot at 69, 0; a dot at 69, 25; a dot at 70, 10; a dot at 71, 30; a dot at 74, 40; and a dot at 76, 25.
C
Image with description A dot plot with the x axis titled Height in Inches begins with 64 and ends at 78 with equal intervals of 4, such as 64, 66, 68, 70, 72, 76,and 78. The y axis titled Residual begins with negative 20 and ends at 20 with equal intervals of 5, such as negative 20, 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 a dot at approximately 65, negative 2; a dot at 67, 3; a dot at 68, negative 8; a dot at 69, negative 7; a dot at 69, 18; a dot at 70, negative 2; a dot at 71, 14; a dot at 74, 10; and a dot at 76, negative 15.
D
Image with description A dot plot with the x axis titled Height in Inches begins with 64 and ends at 78 with equal intervals of 4, such as 64, 66, 68, 70, 72, 76,and 78. The y axis titled Residual begins with negative 40 and ends at 30 with equal intervals of 10, such as negative 40, negative 30, negative 20, negative 10, 0, 10, 20, 30 and 40. A horizontal line parallel to the x axis starts from the point where y is 0. There is a dot at approximately 65, 15; a dot at 66, 15; a dot at 67, 0; a dot at 68, 5; a dot at 69, 0; a dot at 69, negative 25; a dot at 70, negative 10; a dot at 71, negative 30; a dot at 74, negative 40; and a dot at 76, negative 25.
3

The equation of the least-squares regression line is hat y is equal to 16 point 5 plus 8 point 5 1 x , where hat y is the bill for the dinner and x is number of people in the party. Which shows the residual plot?

A
Image with description A dot plot with the x axis titled People begins with 0 and ends at 12 with equal intervals of 2, such as 0, 2, 4, 6, 8, 10, and 12. The y axis titled Residual begins with negative 20 and ends at 30 with equal intervals of 10, such as negative 20, negative 10, 0, 10, 20, 30. A horizontal line parallel to the x axis starts from the point where y is 0. There is a dot at approximately 1, negative 18; a dot at 2, negative 1; a dot at 2, 9; a dot at 3, negative 12; a dot at 3, 9; a dot at 4, negative 1; a dot at 5, 5; a dot at 5, 25; a dot at 6, negative 8; and a dot at 10, negative 9.
B
Image with description A dot plot with the x axis titled People begins with 0 and ends at 12 with equal intervals of 2, such as 0, 2, 4, 6, 8, 10, and 12. The y axis titled Residual begins with negative 60 and ends at 40 with equal intervals of 20, such as negative 60, negative 40, negative 20, 0, 20, and 40. A horizontal line parallel to the x axis starts from the point where y is 0. There is a dot at approximately 1, 38; a dot at 2, 5; a dot at 2, 15; a dot at 3, negative 5; a dot at 3, 15; a dot at 4, negative 1; a dot at 5, negative 19; a dot at 5, negative 40; a dot at 6, negative 15; and a dot at 10, negative 45.
C
Image with description A dot plot with the x axis titled People begins with 0 and ends at 12 with equal intervals of 2, such as 0, 2, 4, 6, 8, 10, and 12. The y axis titled Residual begins with negative 30 and ends at 20 with equal intervals of 10, such as negative 30, negative 20, negative 10, 0, 10, and 20. A horizontal line parallel to the x axis starts from the point where y is 0. There is a dot at approximately 1, 18; a dot at 2, 1; a dot at 2, negative 9; a dot at 3, 12; a dot at 3, negative 9; a dot at 4, 1; a dot at 5, negative 5; a dot at 5, negative 25; a dot at 6, 8; and a dot at 10, 9.
D
Image with description A dot plot with the x axis titled People begins with 0 and ends at 12 with equal intervals of 2, such as 0, 2, 4, 6, 8, 10, and 12. The y axis titled Residual begins with negative 40 and ends at 60 with equal intervals of 20, such as negative 40, negative 20, 0, 20, 40, and 60. A horizontal line parallel to the x axis starts from the point where y is 0. There is a dot at approximately 1, negative 38; a dot at 2, 1; a dot at 2, negative 10; a dot at 3, 5; a dot at 3, negative 18; a dot at 4, 1; a dot at 5, 19; a dot at 5, 40; a dot at 6, 18; and a dot at 10, 45.
4

The equation of the least-squares regression line is hat y is equal to 19 point 2 minus 0 point 8 6 8 x , where hat y is the price of the vehicle (in thousands of dollars) and x is the age (in years). Which shows the residual plot?

A
Image with description A dot plot with the x axis titled Age in Years begins with 0 and ends at 16 with equal intervals of 2, such as 0, 2, 4, 6, 8, 10, 12, 14, and 16. The y axis titled Residual begins with negative 6 and ends at 6 with equal intervals of 2, such as negative 6, negative 4, negative 2, 0, 2, 4, and 6. A horizontal line parallel to the x axis starts from the point where y is 0. There is a dot at approximately 3, 5; a dot at 4, 3; a dot at 5, 0; a dot at 5, 3; a dot at 7, negative 1; a dot at 10, negative 3; and a dot at 15, negative 6.
B
Image with description A dot plot with the x axis titled Age in Years begins with 0 and ends at 16 with equal intervals of 2, such as 0, 2, 4, 6, 8, 10, 12, 14, and 16. The y axis titled Residual begins with negative 6 and ends at 8 with equal intervals of 2, such as negative 6, negative 4, negative 2, 0, 2, 4, 6, and 8. A horizontal line parallel to the x axis starts from the point where y is 0. There is a dot at approximately 3, negative 5; a dot at 4, negative 3; a dot at 5, 0; a dot at 5, negative 3; a dot at 7, 1; a dot at 10, 3; and a dot at 15, 6.
C
Image with description A dot plot with the x axis titled Age in Years begins with 0 and ends at 16 with equal intervals of 2, such as 0, 2, 4, 6, 8, 10, 12, 14, and 16. The y axis titled Residual begins with negative 1 point 5 and ends at 2 point 0 with equal intervals of 0 point 5, such as negative 1 point 5, negative 1 point 0, negative 0 point 5, 0, 0 point 5, 1 point 0, 1 point 5, and 2 point 0. A horizontal line parallel to the x axis starts from the point where y is 0. There is a dot at approximately 3, negative 1 point 4; a dot at 4, negative 0 point 25; a dot at 5, 1 point 75; a dot at 5, negative 1 point 2; a dot at 7, 1 point 2; a dot at 10, 0 point 5; and a dot at 15, negative 0 point 8.
D
Image with description A dot plot with the x axis titled Age in Years begins with 0 and ends at 16 with equal intervals of 2, such as 0, 2, 4, 6, 8, 10, 12, 14, and 16. The y axis titled Residual begins with negative 2 point 0 and ends at 1 point 5 with equal intervals of 0 point 5, such as negative 2 point 0, negative 1 point 5, negative 1 point 0, negative 0 point 5, 0, 0 point 5, 1 point 0, and 1 point 5. A horizontal line parallel to the x axis starts from the point where y is 0. There is a dot at approximately 3, 1 point 4; a dot at 4, 0 point 25; a dot at 5, negative 1 point 75; a dot at 5, 1 point 2; a dot at 7, negative 1 point 2; a dot at 10, negative 0 point 5; and a dot at 15, 0 point 8.
5

The equation of the least-squares regression line is hat y is equal to 2 point 7 plus 1 point 0 4 2 x , where hat y is each son’s height and x is his father’s height. Which shows the residual plot?

A
Image with description A dot plot with the x axis titled Father's Height in Inches begins with 60 and ends at 76 with equal intervals of 2, such as 60, 62, 64, 66, 68, 70, 72, 74, and 76. The y axis titled Residual begins with negative 3 and ends at 5 with equal intervals of 1, such as negative 3, negative 1, negative 1, 0, 1, 2, 3, 4, and 5. A horizontal line parallel to the x axis starts from the point where y is 0. There is 1 dot at approximately 60, 0 point 8; 61, 0 point 6; 63, negative 1 point 2; 1 dot at 63, 2 point 8; 1 dot at 66, negative 1 point 5; 1 dot at 67, negative 2 point 5; 1 dot at 74, negative 2 point 8; and 1 dot at 75, 4 point 2.
B
Image with description A dot plot with the x axis titled Father's Height in Inches begins with 60 and ends at 76 with equal intervals of 2, such as 60, 62, 64, 66, 68, 70, 72, 74, and 76. The y axis titled Residual begins with negative 16 and ends at 4 with equal intervals of 4, such as negative 16, negative 12, negative 8, negative 4, 0, and 4. A horizontal line parallel to the x axis starts from the point where y is 0. There is a dot at approximately 60, 4; a dot at 61, 3; a dot at 63, negative 1; a dot at 63, 3; a dot at 66, 0; a dot at 67, 0; a dot at 74, negative 7; and a dot at 75, negative 15.
C
Image with description A dot plot with the x axis titled Father's Height in Inches begins with 60 and ends at 76 with equal intervals of 2, such as 60, 62, 64, 66, 68, 70, 72, 74, and 76. The y axis titled Residual begins with negative 5 and ends at 3 with equal intervals of 1, such as negative 5, negative 4, negative 3, negative 2, negative 1, 0, 1, 2, and 3. A horizontal line parallel to the x axis starts from the point where y is 0. There is a dot at approximately 60, negative 0 point 8; a dot at 61, negative 0 point 6; a dot at 63, negative 2 point 8; a dot at 63, 1 point 4; a dot at 66, negative 2 point 5; a dot at 67, 2 point 5; a dot at 74, 2 point 8; and a dot at 75, negative 4 point 2
D
Image with description A dot plot with the x axis titled Father's Height in Inches begins with 60 and ends at 76 with equal intervals of 2, such as 60, 62, 64, 66, 68, 70, 72, 74, and 76. The y axis titled Residual begins with negative 4 and ends at 16 with equal intervals of 4, such as negative 4, 0, 4, 8, 12, 16. A horizontal line parallel to the x axis starts from the point where y is 0. There is 1 dot at approximately 60, negative 4; 61, negative 3; 63, negative 3; 1 dot at 63, 1; 1 dot at 66, 0; 1 dot at 67, 0; 1 dot at 74, 7; and 1 dot at 75, 15.
6

An anthropologist is interested in the relationship between fathers’ and sons’ heights. She collects a simple random sample of 25 fathers and 25 sons and determines that the least-squares regression line is hat y is equal to negative 2 point 8 plus 1 point 1 x , where start set hat y end set is the predicted height of each son and x is the height of his father (both measured in inches). One father is 70 inches tall and the residual for his son’s height is 2 point 5 What is the son’s actual height?

A
82 point 3 inches
B
76 point 7 inches
C
71 point 7 inches
D
74 point 2 inches
7

An anthropologist is interested in the relationship between fathers’ and sons’ heights. She collects a simple random sample of 25 fathers and 25 sons, and determines that the least-squares regression line is hat y is equal to negative 2 point 8 plus 1 point 1 x , where start set hat y end set is the predicted height of each son and x is the height of his father (both measured in inches). One father is 72 inches tall, and his son is 75 inches tall. What is the residual for the son’s height?

A
1 point 4
B
1 point 1
C
negative 2 point 8
D
negative 1 point 4
8

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 500 miles and its residual was 115 point 0 0 What was the fare for this flight?

A
102 point 5 0
B
427 point 5 0
C
542 point 5 0
D
312 point 5 0
9

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 scores 75 points. What is the residual for this team during this game?

A
5
B
10
C
65
D
negative 33
10

What is the residual for the rideshare cost with a distance of 5 miles?

A
negative 0 point 3 4
B
2 point 3 3
C
5 point 2 1
D
0 point 3 4

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