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.

(a) Draw a scatter diagram displaying the data.

(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

(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.

(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

	X	Y	X * Y
	1	51	51	1	2601
	4	42	168	16	1764
	5	33	165	25	1089
	6	26	156	36	676
Total	16	152	540	78	6130

Mean   

Mean

Equation of regression line is


b = -4.8571

a =( 152 - ( -4.8571 * 16 ) ) / 4
a = 57.4286
Equation of regression line becomes

Coefficient of determination

Explained variation = 0.933 * 100 = 93.3%

Unexplained variation = 1 - 0.933 = 0.067 * 100 = 6.7%

When X = 3