The Minnesota Department of Transportation installed a state-of-the-art weigh-in-motion scale in the concrete surface of the eastbound

Question:

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 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 the accompanying table), calibration adjustments were made in the software of the weigh-in-motion system, and the scales were reevaluated.

a. Construct two scatter plots, one of y1 versus x and the other of y2 versus x.
b. Use the scatter plots 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.