An owner of a large car lot believes that fuel prices are going to rise significantly and wonders how this rise might affect demand for the high performance vehicles. Specifically, the owner is investigating a link between how fast a car can go from 0 to 60 miles per hour (measured in seconds) and the car's economy as measured in miles traveled per gallon used (mpg). If fast cars, which are normally high in demand, are associated with higher mpg then there will be much less demand if gas prices rise as predicted. The owner gathers data on 20 vehicles. The data is provided below. Use Excel to calculate the correlation coefficient r between the two data sets. Round your answer to two decimal places. "mpg" 0 to 60 time (seconds) 28 7.7 25 8.2 25 8.6 22 7.4 22 8 21 6.9 21 7.5 21 7.4 21 7.8 21 8.8 20 6.1 20 6.9 20 7.2 20 7.5 20 7.5 20 7.5 20 7.7 19 6.7 19 7.9 19 8.5

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MrRoyal MrRoyal · Answer 1 · 2022-08-01T23:24:34+02:00

The correlation coefficient r between the two data sets is 0.33

From the table of values, we make use of the following representations:

Using the above representations, we can now plot our data values in the Excel software

From the Excel application, we have the following summary:

X Values

∑ = 424

Mean = 21.2

∑(X - Mx)2 = SSx = 101.2

Y Values

∑ = 151.8

Mean = 7.59

∑(Y - My)2 = SSy = 8.238

X and Y Combined

N = 20

∑(X - Mx)(Y - My) = 9.54

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

This gives

r = 9.54 / √((101.2)(8.238))

Evaluate

r = 0.3304

Approximate

r = 0.33

Hence, the correlation coefficient r between the two data sets is 0.33

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