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 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, 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 =

(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 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	%

(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.)
%

Answer 1

b)from above given table:

ΣX =	13.000
ΣY=	150.000
ΣX2 =	65.000
ΣY2 =	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 r2 = (-0.986)^2 =				0.972
explained =r2*100=				97.2%
unexplained=(1-r2)*100 =				2.8%

f)from regression equation:

predicted value =49+-3.538*3=

38.39