Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x be the weight of the car (in hundreds of pounds), and let y be the miles per gallon (mpg). The following information is based on data taken from Consumer Reports (Vol. 62, No. 4):

Complete parts (a) through (e), given ˆ‘x = 299, ˆ‘y = 167, ˆ‘x2 = 11,887,
ˆ‘y2 = 3773, ˆ‘xy = 5814, and r ‰ˆ 20.946.
(a) Draw a scatter diagram displaying the data.
(b) Verify the given sums ˆ‘x, ˆ‘y, ˆ‘x2, ˆ‘y2, and ˆ‘xy and the value of the sample correlation coefficient r.
(c) Find x, y, a, and b. Then find the equation of the least-squares line ŷ = α + bx.

(e) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained?
(f) Suppose a car weighs x = 38 (hundred pounds). What does the least-squares line forecast for y = miles per gallon?

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