Data for this problem are based on information from STATS Basketball Scoreboard. 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 that were more than (i.e., over and above) the number of fouls made by the opposing team. Let y be the percentage of times the team with the larger number of fouls won the game.

Complete parts (a) through (e), given ˆ‘x = 13, ˆ‘y = 154, ˆ‘x2 = 65, ˆ‘y2 = 6290,
ˆ‘xy = 411, and r ‰ˆ ˆ’0.988.
(a) Draw a scatter diagram displaying the data.
(b) Verify the given sums ˆ‘x, ˆ‘y, ˆ‘x2, ˆ‘y2, and ˆ‘xy and the value of the sample correlation coefficient r.
(c) Find x, y, a, and b. Then find the equation of the least-squares line ŷ = α + bx.

(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?
(f) If a team had x = 4 fouls over and above the opposing team, what does the
least-squares equation forecast for y?

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