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 "weight-in-motion" scale. To see if the new device was accurate, they conducted a calibration test. They weighed several stopped trucks (Static Weight) and assumed that this weight was correct. Then they weighed the trucks again while they were moving to see how well the new scale could estimate the actual weight. Their data are given in the table at the top of the next column.
Weights (1000s of lbs)
Weight-in-Motion Static Weight
26.0 …………………………… 27.9
29.9 …………………………… 29.1
39.5 …………………………… 38.0
25.1 …………………………… 27.0
31.6 …………………………… 30.3
36.2 …………………………… 34.5
25.1 …………………………… 27.8
31.0 …………………………… 29.6
35.6 …………………………… 33.1
40.2 …………………………… 35.5
a) Make a scatterplot for these data.
b) Describe the direction, form, and strength of the plot.
c) Write a few sentences telling what the plot says about the data. (The sentences should be about weighing trucks, not about scatterplots.)
d) Find the correlation.
e) If the trucks were weighed in kilograms, how would this change the correlation? (1 kilogram = 22 pounds)
f) Do any points deviate from the overall pattern? What does the plot say about a possible recalibration of the weight-in-motion scale?