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 27 46 30 47 23 40 34 52 y 30 20 25 13 29 17 21 14

Complete parts (a) through (e), given Σx = 299, Σy = 169, Σx2 = 11,943, Σy2 = 3861, Σxy = 5880, and

r ≈ −0.923.

(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 = 30 (hundred pounds). What does the least-squares line forecast for y = miles per gallon? (Round your answer to two decimal places.)
mpg

b)

 ΣX = 299 ΣY= 169 ΣX2 = 11943 ΣY2 = 3861 ΣXY = 5880 r = -0.923

c)

 X̅=ΣX/n = 37.38 Y̅=ΣY/n = 21.13 ŷ = 42.365+(-0.568)x

e)

 coefficient of determination r2 = 0.853 explained = 85.3% unexplained= 14.7%

f)

 predicted value =42.365+-0.568*30= 25.33

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