Question

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

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 0 2 5 6 y 48 43 33 26 Complete parts (a) through (e), given Σx = 13, Σy = 150, Σx2 = 65, Σy2 = 5918, Σxy = 407, and r ≈ −0.986.

(b) 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 =

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

(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.)
% b)from above given table:

 ΣX = 13 ΣY= 150 ΣX2 = 65 ΣY2 = 5918 ΣXY = 407 r = -0.986

c)

 X̅=ΣX/n = 3.25 Y̅=ΣY/n = 37.50 ŷ = 49.000+(-3.538)x

e)

 coefficient of determination r2 = (-0.986)^2 = 0.972 explained =r2*100= 97.2% unexplained=(1-r2)*100 = 2.8%

f)from regression equation:

 predicted value =49+-3.538*3= 38.39

#### Earn Coins

Coins can be redeemed for fabulous gifts.