# 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