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 0 4 S 6 33 26 v so 41 50 (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.) Ex = Ey = Ex = Ey? Exy =L (c) Find x, and y. Then find the equation of the least-squares line ý = a + bx. (Round your answers to four decimal places.) y (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. y y 5 55 s0t 50 a a 45 45 40 40 35 35 30 30 25 25 4 6 2 4 6 8 y y 55 50 5 50 45 45 40 40 d 35 35 30 30 25 25 2. 4 (e) Find the value of the coefficient of determination r. 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 to four decimal places. Round your answers for the percentages to two decimal place.) 2- explained

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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.

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.
х
4
5
6
y
50
41
33
26
(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.)
Ex =
Ey =
Ex2 =
Ey? =
Exy =
r =
(c) Find x, and y. Then find the equation of the least-squares line ŷ = a + bx. (Round your answers to four decimal places.)
x =
y =
ŷ =
(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.
y
y
55
55
b
50
50
a
45
45
40
40
35
35
30
30
25
25
X
X
2
4
6
8
2
4
6
8
y
55
55
50
50
45
45
40
40
d
35
35
30
30
25
25
X
2
8
2
4
8
(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 four decimal places.
Round your answers for the percentages to two decimal place.)
12 =
explained
%
unexplained
%
(f) 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.)
%
Transcribed Image Text: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. х 4 5 6 y 50 41 33 26 (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.) Ex = Ey = Ex2 = Ey? = Exy = r = (c) Find x, and y. Then find the equation of the least-squares line ŷ = a + bx. (Round your answers to four decimal places.) x = y = ŷ = (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. y y 55 55 b 50 50 a 45 45 40 40 35 35 30 30 25 25 X X 2 4 6 8 2 4 6 8 y 55 55 50 50 45 45 40 40 d 35 35 30 30 25 25 X 2 8 2 4 8 (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 four decimal places. Round your answers for the percentages to two decimal place.) 12 = explained % unexplained % (f) 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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