2.39 In the summer of 1981, the Minnesota Department of Transportation installed a stateof-

the-art weigh-in-motion scale in the concrete surface of the eastbound lanes of Interstate 494 in Bloomington, Minnesota, The system is computerized and monitors traffic continuously. It is capable of distinguishing among 13 different types of vehicles (car, five-axle semi, five-axle twin trailer, etc.). The primary purpose of the system is to provide traffic counts and weights for use in the planning and design of future roadways. Following installation, a study was undertaken to determine whether the scale’s readings corresponded with 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 table below), calibration adjustments were made in the software of the weigh-in-motion system, and the weigh-in-motion scales were reevaluated

(Wright, Owen, and Pena, “Status of MN/DOT’s”

Weigh-in-Motion Program,” Minnesota DOT, 1983).

r2 r2 r2 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 were 1. Could this happen if the static weights and the weigh-in-motion reading disagreed? Explain.