Residuals Answers
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.
A researcher is studying the relationship between fathers’ and sons’ heights. He collects a simple random sample of eight pairs of fathers and sons and records their heights as shown 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).
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.
A real estate agent is interested in the relationship between the size of a home (measured in square feet) and the selling price of the home. She collects a simple random sample of nine homes in her area and records the size and price of each house. She finds a linear model to give the relationship between the size of the home (measured in thousands of square feet) and the selling price of the home (measured in thousands of dollars). The equation of the line is ŷ = 5102 + 112x, where ŷ is the selling price of the home and x is the square footage. 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).
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.
A coach collects the height and weight of 10 players on the basketball team 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.
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