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 49 44 33 26 Complete parts (a) through (e), given Σx = 13, Σy = 152, Σx2 = 65, Σy2 = 6102, Σxy = 409, and  r ≈ −0.987. (a) Draw a scatter diagram displaying the data.   (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 (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 = 4 fouls over and above the opposing team, what does the least-squares equation forecast for y? (Round your answer to two decimal places.) %

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ISBN:9781119256830
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Chapter1: Starting With Matlab
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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 49 44 33 26

Complete parts (a) through (e), given Σx = 13, Σy = 152, Σx2 = 65, Σy2 = 6102, Σxy = 409, and 

r ≈ −0.987.
(a) Draw a scatter diagram displaying the data.
 

(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

(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 = 4 fouls over and above the opposing team, what does the least-squares equation forecast for y? (Round your answer to two decimal places.)
 %
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