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
30
44
34
47
23
40
34
52
y
32
19
24
13
29
17
21
14
Try parts (a) through (e), given Σx = 304, Σy = 169, Σx2 = 12,190, Σy2 = 3897, Σxy = 6012, and
r ≈ −0.898.

(b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r.
Σx =
Σy =
Σx2 =
Σy2 =
Σxy =
r =

(c) Find x, and y. Then find the equation of the least-squares line  = a + bx. (Round the answers for x and y to two decimal places. Round the 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 answer for r2 to three decimal places. Round answers for the percentages to one decimal place.)
r2 =
explained
%
unexplained
%

(f) Suppose a car weighs x = 36 (hundred pounds). What does the least-squares line forecast for y = miles per gallon? (Round answer to two decimal places.)
mpg

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