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 | 25 | 46 | 32 | 47 | 23 | 40 | 34 | 52 |
y | 29 | 20 | 23 | 13 | 29 | 17 | 21 | 14 |
Complete parts (a) through (e), given Σx = 299, Σy = 166, Σx^{2} = 11,963, Σy^{2} = 3706, Σxy = 5781, and
r ≈ −0.932.
(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 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 = 37 (hundred pounds). What
does the least-squares line forecast for y = miles per
gallon? (Round your answer to two decimal places.)
_________ mpg
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