In: Statistics and Probability
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 | 49 | 44 | 33 | 26 |
Complete parts (a) through (e), given Σx = 16, Σy = 152, Σx2 = 78, Σy2 = 6102, Σxy = 546, and
r ≈ −0.918.
(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.)
%