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 28 42 29 47 23 40 34 52
y 30 17 24 13 29 17 21 14

Complete parts (a) through (e), given Σx = 295, Σy = 165, Σx2 = 11,587, Σy2 = 3701, Σxy = 5650, and

r ≈ −0.945.

(a) Draw a scatter diagram displaying the data.

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

Homework Answers

Answer #1

b)

ΣX = 295.000
ΣY= 165.000
ΣX2 = 11587.000
ΣY2 = 3701.000
ΣXY = 5650.000
r = -0.945

c)

X̅=ΣX/n = 36.88
Y̅=ΣY/n = 20.63
ŷ = 43.221+(-0.613) x

e)

coefficient of determination r2 = 0.894
explained = 89.4%
unexplained= 10.6%

f)

predicted value =43.221+-0.613*31= 24.22
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