Evaluating a truck weigh-in-motion program. The Minnesota Department of Transportation installed a state-of-the-art weigh-in-motion scale in the concrete surface of the eastbound lanes of Interstate 494 in Bloomington, Minnesota. After installation, a study was undertaken to determine whether the scale’s readings correspond to the static weights of the vehicles being monitored. (Studies of this type are known as calibration studies.) After some preliminary comparisons using a two-axle, six-tire truck carrying different loads (see the table at the bottom of the next page), calibration adjustments were made in the software of the weigh-in-motion system, and the scales were reevaluated.

a. Construct two scatterplots, one of y1 versus x and the other of y2 versus x.

b. Use the scatterplots of part a to evaluate the performance of the weigh-in-motion scale both before and after the calibration adjustment.

c. Calculate the correlation coefficient for both sets of data and interpret their values. Explain how these correlation coefficients can be used to evaluate the weigh-in-motion scale.

d. Suppose the sample correlation coefficient for y2 and x was 1. Could this happen if the static weights and the weigh-in-motion readings disagreed? Explain. Trial Number Static Weight of Truck, x (thousand pounds) Weigh-inMotion Reading Prior to Calibration Adjustment, y1 (thousand pounds) Weigh-inMotion Reading After Calibration Adjustment, y2 (thousand pounds) 1 27.9 26.0 27.8 2 29.1 29.9 29.1 3 38.0 39.5 37.8 4 27.0 25.1 27.1 5 30.3 31.6 30.6 6 34.5 36.2 34.3 7 27.8 25.1 26.9 8 29.6 31.0 29.6 9 33.1 35.6 33.0 10 35.5 40.2 35.0