Unit 2 Multiple Choice

Which of the following relationships between two variables could be described using correlation, r?

• Number of books read and gender of a student.

• Number of football games played and the position of a football player.

• High temperature of the day and number of zoo visitors that day.

• Type of beverage ordered and time of day it was ordered.

• Brand of cell phone and number of cell phones sold.

A scatterplot shows a strong, positive, linear relationship between the number of rebounds a basketball team averages and the number of wins that team records in a season. Which conclusion is most appropriate?

• A team that increases its number of rebounds causes its chances of winning more games to increase.

• If the residual plot shows no pattern, then it is safe to conclude that getting more rebounds causes more wins, on average.

• If the residual plot shows no pattern, then it is safe to conclude that getting more wins causes more rebounds, on average.

• If the r² value is close enough to 100%, then it is safe to conclude that getting more rebounds causes more wins, on average.

• Rebounds and wins are positively correlated, but we cannot conclude that getting more rebounds causes more wins, on average.

Two variables, x and y, have a correlation of 0.75. If x has a mean of 25 and a standard deviation of 3, and y has a mean of 12 and a standard deviation of 6, which of the following is the least-squares regression line for the two variables?

• ŷ = −25.5 + 1.5x

• ŷ = 12 + 1.5x

• ŷ = 12 + 0.75x

• ŷ = 16 + 0.75x

• Not enough information

Data are collected on the amount of fat (in grams) and calories in the french fry orders at nine fast food restaurants. The least-squares regression line for the data is ŷ = 274.34 + 9.55x, where ŷ is the predicted number of calories and x is grams of fat. Which of the following is the correct interpretation of the slope of the least-squares regression line?

• The calories increase by 9.55, on average.

• For every increase in fat, the calories increase as well.

• Every increase of 1 gram of fat causes an increase of 9.55 calories.

• For every increase of 1 gram of fat, the predicted calories increase by 9.55.

• For every increase of 1 calorie, the predicted grams of fat increase by 9.55.

The scatterplot below shows data for the nine french fry orders from the previous problem, with the least-squares regression line displayed. Which of the following is the best estimate of the value of the residual for the point indicated by the arrow?

• -570

• 570

• -60

• 60

• 630

The scatterplot below shows data for the nine french fry orders from the previous problem. A tenth fast food chain has been added, as indicated by the arrow. How would this tenth data point affect the slope and correlation in this scenario?

• Slope decreases, correlation increases

• Slope increases, correlation increases

• Slope increases, correlation decreases

• Slope decreases, correlation decreases

• Cannot be determined without the full set of data

Battery life has a strong, negative, linear relationship with temperature. If the least-squares regression line using x = temperature explains 90% of the variation in battery life, which of the following must be the correlation, r, between battery life and temperature?

• -0.90

• 0.90

• -0.95

• 0.95

• Cannot be determined without the original data.

Which of the following is the equation of the least-squares regression line?

• ŷ = 19.31 + 0.891x

• ŷ = 2.8621 + 0.2715x

• ŷ = 0.891 + 19.31x

• ŷ = 0.2715 + 2.8621x

• ŷ = 0.2715 + 0.891x

Which of the following is a correct interpretation of r²?

• (A) Number of hours of television explains 30% of the variability in power consumption.

• (B) 30% of the increase in number of hours of television is explained by power consumption.

• (C) 30% of the data will lie on the least-squares regression line.

• (D) 30% of the residuals will be less than 4.185.

• (E) All of the above are correct interpretations.

Using the least-squares regression line, ŷ = -25.5 + 1.5x, what is the residual for the data point at (28, 19)?

• -2.5

• 2.5

• 4.33

• 16.5

• 19