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?
Substitute the father’s height, 72 inches, into the regression line: the predicted son’s height is −2.8 + 1.1(72) = 76.4 inches. A residual is observed height minus predicted height, so 75 − 76.4 = −1.4 inches; the correct choice is negative 1.4.
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