Residuals Answers

Jim has started a new exercise program. He has monthly checkups where his percentage of body fat is measured. Jim records his body fat percentage and the number of months he has been on the exercise program. He collects data for 10 months and finds a linear model to give the relationship between the time spent exercising and his percentage of body fat. The equation of the line is ŷ = 17 – 1.25x, where ŷ is his percentage of body fat and x is the time spent exercising (in months). 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.

A student is interested in the depth of the water off the end of the local pier. Starting at midnight, he measures the depth of the water every three hours for an entire day and records the results in the table.

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 nutritionist is curious about how the concentration of a vitamin supplement changes as a function of time (in hours) since a pill has been swallowed. The nutritionist measures the concentration for six hours after the pill was swallowed. He calculates the equation of the least-squares regression line as ŷ = 0.0093 – 0.00121x where ŷ is the concentration and x is the number of hours since the pill was swallowed. The graph shown is the residual plot for this model where the residuals are measured in parts per thousand.

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 statistics student is interested in the relationship between the number of aunts and uncles a person has and the number of cousins. She surveys a simple random sample of 12 people and asks them how many of each they have. She calculates the least-squares regression line and finds the equation is ŷ = 2.6 + 1.64x, where ŷ is the number of cousins and x is the number of aunts and uncles. The residual plot is shown.

A used car dealership is interested in the age of a used car and the price of the vehicle. The manager collects a simple random sample of vehicles as shown in the table.

A restaurant is interested in the relationship between the number of people in a party and the bill for their dinner. An owner of a restaurant records the number of people in the party and the bill for 10 groups of people as shown in the table.

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