Vehicle weights. The Minnesota Department of Transportation hoped that they could measure the weights of big trucks without actually stopping the vehicles by using a newly developed “weigh-in-motion” scale. After installation of the scale, a study was conducted to find out whether the scale’s readings correspond to the true weights of the trucks being monitored. In Exercise 40 of Chapter 7, you examined the scatterplot for the data they collected, finding the association to be approximately linear with . Their regression equation is  where both the scale reading and the predicted weight of the truck are measured in thousands of pounds.

a) Estimate the weight of a truck if this scale read 31,200 pounds.

b) If that truck actually weighed 32,120 pounds, what was the residual?

c) If the scale reads 35,590 pounds, and the truck has a residual of pounds, how much does it actually weigh?

d) In general, do you expect estimates made using this equation to be reasonably accurate? Explain.

e) If the police plan to use this scale to issue tickets to trucks that appear to be overloaded, will negative or positive residuals be a greater problem? Explain.

Exercise 40

Profit. How are a company’s profits related to its sales? Let’s examine data from 71 large U.S. corporations. All amounts are in millions of dollars. a) Histograms of Profits and Sales and histograms of the logarithms of Profits and Sales are on the next page. Why are the re-expressed data better for regression?

b) Here are the scatterplot and residuals plot for the regression of logarithm of Profits vs. log of Sales. Do you think this model is appropriate? Explain.

c) Here’s the regression analysis. Write the equation.

d) Use your equation to estimate profits earned by a company with sales of 2.5 billion dollars. (That’s 2500 million.)