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 51 41 33 26 Complete parts (a) through (e), given Σx = 13, Σy = 151, Σx2 = 65, Σy2 = 6047, Σxy = 403, and r ≈ −0.9880. (a) Draw a scatter diagram displaying the data.
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 | 51 | 41 | 33 | 26 |
Complete parts (a) through (e), given Σx = 13, Σy = 151, Σx2 = 65, Σy2 = 6047, Σxy = 403, and
| 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 to four 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 four decimal places. Round your answers for the percentages to two 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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