Linear Regression Multiple Choice Practice

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 $r^2$ 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.

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 shown to the left. 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 at left 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.

A random sample of households is taken. For each household, the number of hours spent watching television and the power consumption (in kWh) during a day are recorded. The table at left shows computer output from a linear regression analysis on the data. Which of the following is the equation of the least-squares regression line?

• 
• 
• 
• 
• 

A random sample of households is taken. For each household, the number of hours spent watching television and the power consumption (in kWh) during a day are recorded. The table at left shows computer output from a linear regression analysis on the data. Which of the following is a correct interpretation of  $r^2$   ? 

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

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

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

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

• All of the above are correct interpretations. 

Using the least-squares regression line shown at left, what is the residual for the data point at (28,19)?

• -2.5

• 2.5

• 4.33

• 16.5

• 19

Shown at left is computer output from the least squares regression analysis on the body mass index, BMI, and percent body fat for 10 randomly selected adult males. Which of the following represents the 95% confidence interval for the slope of the regression line relating BMI and percent body fat for the population of adult males?

• -20.096 $\pm$ 2.21(2.786)

• 1.695 $\pm$ 7.432(0.2280)

• 1.695 $\pm$ 2.306(0.2280)

• 1.695 $\pm$ 2.262(0.2280)

• 1.695 $\pm$ 2.228(0.2280)

A financial analyst wants to investigate the relationship between the annual starting salary of new employees at a large firm versus years of education the employee has (beyond high school). The analyst selected a random sample of 18 new employees and recorded their starting salary and how many years of education they have beyond high school. The computer output of an analysis of salary versus years of education is shown in the table. Assuming that all conditions for inference are met, which of the following is the appropriate test statistic for testing the null hypothesis that the slope of the population regression line equals 0?

• 0

• 0.163

• 1

• 1.54

• 25.40

As the temperature rises in Chicago, does the crime rate also rise? Using data available from the Chicago Police Department, an interested citizen recorded the high temperature and number of crimes reported for 8 randomly selected days. The citizen wants to find a confidence interval that can be used to estimate the number of additional crimes that can be expected to be reported for each degree that the daily high temperature increases with 95% confidence. Which of the following is the most appropriate procedure for such an investigation?

• A chi-square test of association

• A linear regression t-interval for slope

• A one-sample t-interval for a mean

• A two-sample t-interval for a difference of means

• A one-sample z-interval for a proportion