Study Guide #6 It is thought that basketball teams that make too many fouls in a
ID: 2908944 • Letter: S
Question
Study Guide #6
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.
Complete parts (a) through (e), given ?x = 16, ?y = 152, ?x2 = 78, ?y2 = 6102, ?xy = 546, and r ? ?0.918.
(b) Verify the given sums ?x, ?y, ?x2, ?y2, ?xy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)
(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.)
(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.)
%
Explanation / Answer
b)
verify yourself
c)
xbar = 1/4 ( 1 + 4 + 5 +6) = 4
ybar = 1/4 (49 + 44 + 33+ 26) = 38
y^ = 55.7143 - 4.4286* x
d)
option B) is correct {top right}
note the intercept is 55.7143
e)r^2 = 0.8422
hence
explained = 84.2 %
unexplained = 100 - 84.2 = 15.8
f)
x = 3
y^ = 55.7143 - 4.4286* 3
= 42.4285
= 42.43