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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).

 x 27 43 32 47 23 40 34 52 y 29 22 22 13 29 17 21 14

Complete parts (a) through (e), given Σx = 298, Σy = 167, Σx2 = 11,800, Σy2 = 3745, Σxy = 5833, and

r ≈ −0.911.
(a) Draw a scatter diagram displaying the data.

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(b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)
 Σx = Σy = Σx2 = Σy2 = Σxy = r =

(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 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 r2 to three decimal places. Round your 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 your answer to two decimal places.)
mpg

3.It is thought that basketball teams that make too many fouls in a game tend to lose the game even if they otherwise play well. Let x be the number of fouls more than (i.e., over and above) the opposing team. Let y be the percentage of times the team with the larger number of fouls wins the game.
 x 1 4 5 6 y 51 44 33 26
Complete parts (a) through (e), given Σx = 16, Σy = 154, Σx2 = 78, Σy2 = 6302, Σxy = 548, and
r ≈ −0.941.
(a) 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 r2 to three decimal places. Round your answers for the percentages to one decimal place.)
 r2 = explained % unexplained %

(b) If a team had x = 3 fouls over and above the opposing team, what does the least-squares equation forecast for y? (Round your answer to two decimal places.)
%
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Step 1

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Given data of x the weight of car and y miles per gallon  and its scatter plot is shown below. help_outlineImage Transcriptionclose35 29 29 30 25 22 21 17 14 13 15 5 0 40 0 10 20 30 50 60 Weight (x) 40 34 43 27 32 47 23 52 29 14 22 13 29 17 21 22 22 10 (A) Jad sallu fullscreen
Step 2

From given data we calculate the required sums to and use the correlation coefficient f... help_outlineImage Transcriptionclosex^2 y^2 841 Χ V 27 29 1 729 783 43 2 22 1849 484 946 3 32 1024 22 484 704 47 2209 611 13 169 23 5 29 529 841 667 40 17 1600 6 289 680 7 1156 34 21 441 714 S 52 14 2704 196 728 Total Σx= 29s Σy-167 Σx211800| Σy2=3745| Σxν= 583 n (Σxw)-(Σ )(Σy) ν(Σ- (Σ)' (ΟΣy - (Σy)') 8(5833)-(298167) (8*11800-(298) )(8*3745-(167^ 2) r =0.911 fullscreen

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