The Minnesota Department of Transportation would like to measure the weights of trucks on its highways without the expense of maintaining weigh stations along the highway. Weigh stations are expense to operate, delay shipments and aggravate truckers. To see if a proposed weight system was accurate transportation officials conducted a test. They weighted trucks when stopped on a regular scale. They then used the remote system to estimate the weights. Here are the data:
Weigh of a truck (thousands of pounds)
New System Scale Weight
1 26 27.9
2 29.9 29.1
3 39.5 38
4 25.1 27
5 31.6 30.3
6 36.2 34.5
7 25.1 27.8
8 31 29.6
9 35.6 33.1
10 40.2 35.5
TOTALS 320.2 312.8
(a) Make a scatter plot of these data and describe the direction, form, and scatter of the plot.
(b) Find the correlation.
(c) If the trucks were weighed in kilograms, how would this change the correlation? (1 kilogram=2.2 pounds)
(d) Interpret the correlation in the context of trucks and weights. What does the correlation tell the Minnesota Department of Transportation?