Residuals Answers

An educator is interested in the relationship between how many hours students spend doing homework and the scores earned on exams. He gathers data from 12 students and calculates the least-squares regression line to be ŷ = 68.4 + 1.46x, where ŷ is the score on an exam and x is the number of hours spent doing homework. The residual plot is shown.

An engineer is interested in the relationship between the weight of a car (measured in pounds) and the fuel economy (measured in miles per gallon of gas). To investigate the relationship, she collects a simple random sample of 10 cars and records their weight and fuel efficiency. She finds the equation of the least-squares regression line to be ŷ = 69 – 0.0114x, where ŷ is the fuel efficiency (mpg) and x is the weight (in pounds). The residual plot is shown.

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 ŷ = –2.8 + 1.1x, where ŷ is the predicted height of each son and x is the height of his father (both measured in inches).

A coach collects the height and weight of 10 players on the basketball team as shown in the table.