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.

x	1	2	5	6
y	48	44	33	26

Complete parts (a) through (e), given Σx = 14, Σy = 151, Σx² = 66, Σy² = 6005, Σxy = 457, and r ≈ −0.993.

(a) 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 =

(b) 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

(c) 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 =    %

(d) 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.)

= %

Answer 1