6
QuizMultiple Choice

Residuals — Quiz

Question 6 • Statistical Reasoning

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?

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

Explanation

First find the predicted height: −2.8 + 1.1(70) = 74.2 inches. A residual is actual height minus predicted height, so the son's actual height is 74.2 + 2.5 = 76.7 inches. The correct choice is C, 76.7 inches.

AI-written and checked against the verified answer.

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