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...

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	50	44	33	26

Complete parts (a) through (e), given Σx
= 13, Σy
= 153, Σx
²
= 65, Σy
²
= 6201, Σxy
= 409, and

r ≈ −0.991.

(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
= 4 fouls over and above the opposing team, what does the least-squares equation forecast for
y? (Round your answer to two decimal places.)
%

Jun 01, 2022

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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...

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