Residuals Answers

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.

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

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 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.

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 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.

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.

Based on data taken from airline fares and distances flown, it is determined that the equation of the least-squares regression line is ŷ = 102.50 + 0.65x, where ŷ is the predicted fare and x is the distance, in miles. One of the flights was 500 miles and its residual was 115.00.