AP Stats and Power

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 below shows computer output from a linear regression analysis on the 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

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 below shows computer output from a linear regression analysis on the data. Which of the following is a correct interpretation of r²?

• 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.

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.

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

• A

• B

• C

• D

• E

• A

• B

• C

• D

• E

These symbols represent the mean and standard deviation for which of the following distributions?

• The Population

• The Sample

• The Sampling Distribution

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 y = 274.34 + 9.55x, where y 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 shows data for the nine french fry orders, 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

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

• -2.5

• 2.5

• 4.33

• 16.5

• 19