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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).

x 30 42 34 47 23 40 34 52 y 30 17 26 13 29 17 21 14

Complete parts (a) through (e), given x = 302, y = 167, x² = 12,018, y² = 3801, xy = 5898, and r 0.921.

(a) Draw a scatter diagram displaying the data.

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(b) Verify the given sums x, y, x², y², xy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.) x = y = x² = y² = xy = r =

(c) Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.) x = y = = + x

(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.

(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? (Round your answer for r² to three decimal places. Round your answers for the percentages to one decimal place.) r² = explained % unexplained %

(f) Suppose a car weighs x = 34 (hundred pounds). What does the least-squares line forecast for y = miles per gallon? (Round your answer to two decimal places.)

mpg