Question

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.)
%

Answer 1

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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
	r²	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