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 47 32 47 23 40 34 52 y 29 18 23 13 29 17 21 14 Complete parts (a) through (e), given Ex = 301, Ey = 164, Ex2 = 12,107, Ey2 = 3,630, Exy = 5,736, and r= -0.9492. %3D %3D (a) Draw a scatter diagram displaying the data. (b) Verify the given sums Ex, Ey, Ex², Ey², Exy, and the value of the sample correlation coefficient r. (c) Find x, and y. Then find the equation of the least-squares line ŷ = a + bx.

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7)
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).
26
47
32 47
23
40
34
52
y
29
18
23
13
29
17
21
14
Complete parts (a) through (e), given Ex = 301, Ey = 164, Ex2
= 12,107, Ey? = 3,630, Exy = 5,736, andr= -0.9492.
%3D
(a) Draw a scatter diagram displaying the data.
(b) Verify the given sums Ex, Ey, Ex², Ey², Exy, and the value of
the sample correlation coefficient r.
(c) Find x, and y. Then find the equation of the least-squares line
3а + bx.
(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?
(f) Suppose a car weighs x = 38 (hundred pounds). What does
the least-squares line forecast for y = miles per gallon?
Transcribed Image Text: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). 26 47 32 47 23 40 34 52 y 29 18 23 13 29 17 21 14 Complete parts (a) through (e), given Ex = 301, Ey = 164, Ex2 = 12,107, Ey? = 3,630, Exy = 5,736, andr= -0.9492. %3D (a) Draw a scatter diagram displaying the data. (b) Verify the given sums Ex, Ey, Ex², Ey², Exy, and the value of the sample correlation coefficient r. (c) Find x, and y. Then find the equation of the least-squares line 3а + bx. (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? (f) Suppose a car weighs x = 38 (hundred pounds). What does the least-squares line forecast for y = miles per gallon?
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