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 26 43 29 47 23 40 34 52

y 33 18 27 13 29 17 21 14

Complete parts (a) through (e), given x = 294, y = 172, x² = 11,564, y² = 4078, xy = 5815, and r 0.942.

(a) Draw a scatter diagram displaying the data.

(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 = ______

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 = 31 (hundred pounds). What does the least-squares line forecast for y = miles per gallon? (Round your answer to two decimal places.)

_______ mpg