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 29 44 33 47 23 40 34 52…

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 29 44 33 47 23
40 34 52 y 32 20 26 13 29 17 21 14 Complete parts (a) through (e),
given Σx = 302, Σy = 172, Σx2 = 12,064, Σy2 = 4036, Σxy = 6066, and
r ≈ −0.902. (a) Draw a scatter diagram displaying the data. Flash
Player version 10 or higher is required for this question. You can
get Flash Player free from Adobe’s website. (b) Verify the given
sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation
coefficient r. (Round your value for r to three decimal places.) Σx
= Σy = Σx2 = Σy2 = Σxy = 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 = 45 (hundred pounds). What does the least-squares line
forecast for y = miles per gallon? (Round your answer to two
decimal places.) mpg