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QuizMultiple Choice

Residuals — Quiz

Question 1 • Statistical Reasoning

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?

Answer
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.
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