3.7 Warm Up [Stats]

• A cow of 5 years is predicted to produce 5.5 fewer gallons per week.

• A cow of 5 years is predicted to produce 5.5 more gallons per week.

• A cow of 5 years is predicted to produce 1.1 fewer gallons per week.

• A cow of 5 years is predicted to produce 1.1 more gallons per week.

• A cow of 5 years and a cow of 10 years are both predicted to produce 40.8 gallons per week.

The following scatterplot shows two variables, x and y, along with a least-squares model. Which of the following is a high leverage point with respect to the regression?

• (5, 8)

• (20, 31)

• (27, 22)

• (30, 60)

• (80, 70)

Tucker competed in a jigsaw puzzle competition where participants are timed on how long they take to complete puzzles of various sizes. Tucker completed a small puzzle in 75 minutes and a large jigsaw puzzle in 140 minutes. For all participants, the distribution of completion time for the small puzzle was approximately normal with mean 60 minutes and standard deviation 15 minutes. The distribution of completion time for the large puzzle was approximately normal with mean 180 minutes and standard deviation 40 minutes. Approximately what percent of the participants had finishing times greater than Shalise’s for each puzzle?

• 16% on the small puzzle and 16% on the large puzzle

• 16% on the small puzzle and 84% on the large puzzle

• 32% on the small puzzle and 68% on the large puzzle

• 84% on the small puzzle and 84% on the large puzzle

• 84% on the small puzzle and 16% on the large puzzle

For a specific species of fish in a pond, Marcus wants to build a regression equation to predict the weight of a fish based on its length. Marcus collects a random sample of this species of fish and finds that the lengths vary from 0.75 to 1.35 inches. Marcus uses the data from the sample to create a single linear regression model. Would it be appropriate to use this model to predict the weight of a fish of this species that is 3 inches long?

• Yes, because 3 inches falls above the maximum value of lengths in the sample.

• Yes, because the regression equation is based on a random sample.

• Yes, because the association between length and weight is positive.

• No, because 3 inches falls above the maximum value of lengths in the sample.

• No, because there may not be any 3-inch fish of this species in the pond.

Gaby believes that there is a linear relationship between the thickness of an air filter and the amount of particulate matter that gets through the filter; that is, less pollution should get through thicker filters. Gaby tests many filters of different thickness and fits a linear model. If a linear model is appropriate, what should be apparent in the residual plot?

• There should be a positive, linear association in the residual plot.

• There should be a negative, linear association in the residual plot.

• All of the points must have residuals of 0.

• There should be no pattern in the residual plot.

• The residuals should have a small amount of variability for low values of the predictor variable and larger amounts of variability for high values of the predictor variable.