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 2 5 6 y 48 43 33 26 Complete parts (a) through (e), given Σx = 13, Σy = 150, Σx2 = 65, Σy2 = 5918, Σxy = 407, and r ≈ −0.986.
(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.)
%
b)from above given table:
ΣX = | 13.000 |
ΣY= | 150.000 |
ΣX^{2} = | 65.000 |
ΣY^{2} = | 5918.000 |
ΣXY = | 407.000 |
r = | -0.986 |
c)
X̅=ΣX/n = | 3.25 |
Y̅=ΣY/n = | 37.50 |
ŷ = | 49.000+(-3.538)x |
e)
coefficient of determination r^{2} = (-0.986)^2 = | 0.972 | |||
explained =r^{2}*100= | 97.2% | |||
unexplained=(1-r^{2})*100 = | 2.8% |
f)from regression equation:
predicted value =49+-3.538*3= | 38.39 |
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