Question

In: Statistics and Probability

It is thought that basketball teams that make too many fouls in a game tend to...

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 42 33 26

A. given Σx = 16, Σy = 152, Σx2 = 78, Σy2 = 6130, Σxy = 540, and r ≈ −0.966

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 =

B. 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

C. 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     %


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.)
%

Solutions

Expert Solution

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Σx = 16

Σy = 152

Σx2 = 78

Σy2 = 6130

Σxy = 540

r = −0.966

B. 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 bar=16/4 4
y bar=152/4 38
y= 57.429 +(-4.857) x

y=57.429+(-4.857)x

C. 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 0.933
explained     93.3%
unexplained     6.7%

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.)
42.86%

Using Excel<data<data analysis<regression

Regression Analysis
0.933
r   -0.966
Std. Error   3.443
n   4
k   1
Dep. Var. y
ANOVA table
Source SS   df   MS F p-value
Regression 330.2857 1   330.2857 27.86 .0341
Residual 23.7143 2   11.8571
Total 354.0000 3  
Regression output confidence interval
variables coefficients std. error    t (df=2) p-value 95% lower 95% upper
Intercept 57.429 4.06 14.13 0.00 39.94 74.91
x -4.857 0.9203 -5.278 .0341 -8.8168 -0.8974
Predicted values for: y
95% Confidence Interval 95% Prediction Interval
x Predicted lower upper lower upper Leverage
3 42.857 34.457 51.257 25.826 59.888 0.321

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