Question

# Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x...

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 25 46 32 47 23 40 34 52 y 29 20 23 13 29 17 21 14

Complete parts (a) through (e), given Σx = 299, Σy = 166, Σx2 = 11,963, Σy2 = 3706, Σxy = 5781, and

r ≈ −0.932.

(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 = 37 (hundred pounds). What does the least-squares line forecast for y = miles per gallon? (Round your answer to two decimal places.)
_________ mpg

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