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    2    5    6
y    50    44    33    26
Complete parts (a) through (e), given Σx = 14, Σy = 153, Σx2 = 66, Σy2 = 6201, Σxy = 459, and
r ≈ −0.994.
(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 y^= 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    =
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 = 4 fouls over and above the opposing team, what does the least-squares equation forecast for y? (Round your answer to two decimal places.)
%

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