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

Complete parts (a) through (e), given Σx = 16, Σy = 152, Σx² = 78, Σy² = 6130, Σxy = 540, and

r ≈ −0.966.

(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)

ΣX =	16.000
ΣY=	152.000
ΣX2 =	78.000
ΣY2 =	6130.000
ΣXY =	540.000
r =	-0.966

c)

X̅=ΣX/n =	4.00
Y̅=ΣY/n =	38.00
ŷ =	57.429+-4.857x

e)

coefficient of determination r2 =				0.933
explained =				93.3%
unexplained=				6.7%

f)

predicted value =57.429+-4.857*3=

42.86