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 | 5 | 6 |
y | 51 | 42 | 33 | 26 |
Complete parts (a) through (e), given Σx = 15, Σy = 152, Σx^{2} = 77, Σy^{2} = 6130, Σxy = 489, and
r ≈ −0.945.
(b) Verify the given sums Σx, Σy, Σx^{2}, Σy^{2}, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)
Σx = | |
Σy = | |
Σx^{2} = | |
Σy^{2} = | |
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 |
(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) 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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