It is thought that basketball teams that make too many fouls ina game tend to lose the game even if they otherwise play well. Letx be the number of fouls more than (i.e., over and above)the opposing team. Let y be the percentage of times theteam with the larger number of fouls wins the game.
Complete parts (a) through (e), given ?x = 16,?y = 152, ?x2 = 78,?y2 = 6130, ?xy = 540, and
r ? ?0.966.
(a) Draw a scatter diagram displaying the data.
(b) Verify the given sums ?x, ?y,?x2, ?y2, ?xy, andthe value of the sample correlation coefficient r. (Roundyour value for r to three decimal places.)
?x = | |
?y = | |
?x2 = | |
?y2 = | |
?xy = | |
r = | |
(c) Find x, and y. Then find the equation of theleast-squares line = a + bx. (Round your answersfor x and y to two decimal places. Round youranswers for a and b 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 determinationr2. What percentage of the variation iny can be explained by the corresponding variationin x and the least-squares line? What percentage isunexplained? (Round your answer for r2to three decimal places. Round your answers for the percentages toone decimal place.)
r2 = | |
explained    | % |
unexplained    | % |
(f) If a team had x = 3 fouls over and above the opposingteam, what does the least-squares equation forecast for y?(Round your answer to two decimal places.)
%
