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 | 45 | 34 | 47 | 23 | 40 | 34 | 52 |
y
| 31 | 20 | 22 | 13 | 29 | 17 | 21 | 14 |
Complete parts (a) through (e), given Σx
= 301, Σy
= 167, Σx
2
= 12,055, Σy
2
= 3781, Σxy
= 5854, and
r ≈ −0.926.
(b) Verify the given sums Σx, Σy, Σx
2, Σy
2, Σxy, and the value of the sample correlation coefficient
r. (Round your value for
r
to three decimal places.)
(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.)
(e) Find the value of the coefficient of determination
r
2. 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
r
2
to three decimal places. Round your answers for the percentages to one decimal place.)
r
2
= | ? |
| explained | ?% |
| unexplained | ?% |
(f) Suppose a car weighs
x
= 43 (hundred pounds). What does the least-squares line forecast for
y
= miles per gallon? (Round your answer to two decimal places.)
mpg