It is thought that basketball teams that make too many fouls in a game tend to l

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.

Complete parts (a) through (e), given ?x = 15, ?y = 152, ?x2 = 77, ?y2 = 6130, ?xy = 489, and r ? ?0.945.

(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.)
%

x 0 4 5 6 y 51 42 33 26

Explanation / Answer

Solutionb

Sums are verified

Solutionb:

Figure B

Solutionc:

y=52.64-3.90x

Solutione:

R sq=0.893

explained=89.3%

unexpalined=10.7%

Solutionf:

we have

y=52.64-3.90x

for x=3

y=52.64-3.90*3

y=40.94

x y x^2 y^2 xy 0 51 0 2601 0 4 42 16 1764 168 5 33 25 1089 165 6 26 36 676 156 total 15 152 77 6130 489

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