Basketball: Fouls 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 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 50 45 33 26
Complete parts (a) through (e), given Ex=13,Ey=154,Ex^2=65,Ey^2=6290,Exy=411, and r = -0.988.
(f) If a team had x 4 fouls over and above the opposing team, what does the
least-squares equation forecast for y?
(a) Draw a scatter diagram displaying the data.
(b) Verify the given sums Ex,Ey,Ex^2,Ey^2,and Exy and the value of the sample correlation
(c) Find x,y, a, and b. Then find the equation of the least squares line y^= a+bx.
(d) Graph the least-squares line on your scatter diagram. Be sure to use the point (x/, y/)as one of the points on the line.
(e) Find the value of the coefficient of determination r^2. 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
This is my first time doing the kind of problem so I am hoping to use this as a guide to doing the other problems.
The solution determines the effects of fouls on basketball game outcomes.