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 50 44 33 26

Complete parts (a) through (e), given x = 16, y = 153, x2 = 78, y2 = 6201, xy = 547, and r 0.930.

(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.)

x =

y =

x2 =

y2 =

xy =

r =

(c) Find x, and y. Then find the equation of the least-squares line y hat = 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 hat = + 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.)

%