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).

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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).
(b) Verify the given sums Ex, Ey, Ex?, Ey?, Exy, and the value of the sample correlation coefficient r. (Round your value for r to four decimal places.)
Σχ -
Ey =
Ex2 =
Ey2 =
Σχy -
r =
(c) Find x, and y. Then find the equation of the least-squares line ý = a + bx. (Round your answers to four decimal places.)
X =
y =
(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.
y
y
y
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a
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С 201
d
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O-10
O0-10
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O-10
(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 2 to four decimal places.
Round your answers for the percentages to two decimal place.)
2 =
explained
%
unexplained
%
(f) Suppose a car weighs x = 35 (hundred pounds). What does the least-squares line forecast for y = miles per gallon? (Round your answer to two decimal places.)
mpg
Transcribed Image Text:(b) Verify the given sums Ex, Ey, Ex?, Ey?, Exy, and the value of the sample correlation coefficient r. (Round your value for r to four decimal places.) Σχ - Ey = Ex2 = Ey2 = Σχy - r = (c) Find x, and y. Then find the equation of the least-squares line ý = a + bx. (Round your answers to four decimal places.) X = y = (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. y y y 50 50 50 50 40 40 40 40 a 30 30 30 30 С 201 d 20 20 20 10 10 10 10 10 20 30 40 50 60 10 20 30 40 50 60 10 20 30 40 50 60 10 20 30 40 50 60 O-10 O0-10 @0-10 O-10 (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 2 to four decimal places. Round your answers for the percentages to two decimal place.) 2 = explained % unexplained % (f) Suppose a car weighs x = 35 (hundred pounds). What does the least-squares line forecast for y = miles per gallon? (Round your answer to two decimal places.) mpg
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).
х
29
44 33
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y
30
19 24
13
29
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14
Complete parts (a) through (e), given Ex = 302, Ey = 167, Ex? = 12,064, Ey? = 3773, Exy = 5898, and rx -0.9312.
(a) Draw a scatter diagram displaying the data.
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). х 29 44 33 47 23 40 34 52 y 30 19 24 13 29 17 21 14 Complete parts (a) through (e), given Ex = 302, Ey = 167, Ex? = 12,064, Ey? = 3773, Exy = 5898, and rx -0.9312. (a) Draw a scatter diagram displaying the data.
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