Question

The National Basketball Association (NBA) records a variety of statistics for each team. Five of these statistics are he percentage of games won (Win %), the percentage of field goals made (FG%), the percentage of three-point shots made (3P%), the percentage of the free throws made (FT%), the average number of offensive rebounds per game (RBOff), and the average number of defensive rebounds per game (RBDef). The data given in the table below show the values of these statistics for the 30 teams in the NA for one full season. Team Win% FG% 3P% FT% RBOff RBDef Atlanta 60.5 45.4 37.0 74.1 9.9 31.3 Boston 59.0 46.0 36.6 77.7 7.7 31.0 Brooklyn 33.3 42.5 34.2 77.7 11.9 28.5 Charlotte 10.6 41.4 29.5 74.6 10.3 28.7 Chicago 75.8 45.2 37.5 72.2 13.9 32.8 Cleveland 31.8 42.2 34.6 71.6 12.7 29.5 Dallas 54.5 44.3 33.9 77.1 10.1 32.7 Denver 57.6 47.6 33.2 73.5 11.2 31.9 Detroit 37.9 43.8 34.6 75.2 11.7 28.5 Golden State 34.8 45.7 38.8 77.0 9.7 29.5 Houston 51.5 44.9 35.9 78.2 11.7 30.5 Indiana 63.6 43.8 36.8 78.2 12.5 31.4 LA Clippers 60.6 45.5 35.7 68.0 12.1 29.4 LA Lakers 62.1 45.7 32.6 75.6 12.1 34.1 Memphis 62.1 44.7 32.6 75.9 12.6 29.5 Miami 69.7 46.9 35.9 77.5 10.4 31.2 Milwaukee 47.0 44.3 34.5 77.4 12.4 30.0 Minnesota 39.4 43.3 33.2 77.1 12.1 31.7 New Orleans 31.8 45.1 33.3 75.7 11.0 30.2 New York 54.5 44.3 33.6 74.1 11.3 30.5 Oklahoma City 71.2 47.1 35.8 80.6 11.0 32.7 Orlando 56.1 44.1 37.5 66.0 11.2 31.2 Philadelphia 53.0 44.8 36.2 74.2 10.7 32.5 Phoenix 50.0 45.8 34.3 75.7 10.9 30.8 Portland 42.4 44.3 34.6 79.6 11.1 29.5 Sacramento 33.3 43.6 31.6 73.6 13.4 29.5 San Antonio 75.8 47.8 39.3 74.8 10.3 32.6 Toronto 34.8 44.0 34.0 77.0 10.6 31.4 Utah 54.5 45.6 32.3 75.4 13.0 31.1 Washington 30.3 44.1 32.0 72.7 11.7 29.9 a. Develop an estimated regression equation that can be used to predict the percentage of games won given the percentage of field goals made (to 4 decimals). y^ = - _____ + _____ FG% At the .05 level of significance, test for a significant relationship. [- Select your answer -] There is a significant relationship / There is no significant relationship b. Provide the interpretation for the slope of the estimated regression equation developed in part (a). An increase in the percentage of field goals made will [ - Select your answer -] increase / decrease    the percentage of games won. c. Develop an estimated regression equation that can be used to predict the percentage of games won given the percentage of field goals made, the percentage of three-point shots made, the percentage of the free throws made, the average number of offensive rebounds per game, and the average number of defensive rebounds per game (to 4 decimals). y^ = - ___ + ____ FG% + _____ 3P% + ____ FT% + _____ RBOff% + _____ RBDef% d. For the estimated regression equation developed in part (c), remove any independent variables that are not significant at the .05 level of significance and develop a new estimated regression equation using the remaining independent variables (to 4 decimals). y^ = - ___ + ___ [select your answer] (3P%, FT%, RBOff%, RBDef%,GF%) + ___ [ select your answer] (3P%, FT%, RBOff%, RBDef%,GF%) + ___ (3P%, FT%, RBOff%, RBDef%,GF%) + ___ (3P%, FT%, RBOff%, RBDef%,GF%) e. Assuming the estimated regression equation developed in part (d) can be used for the 2012-2013 season, predict the percentage of the games won for a team with the following values for the four independent variables: FG= 45, 3P% = 35, RBOff% = 12, and RBDef = 30 (to 1 decimals). y^ = ___ %

Answer 1

a)

Y^ = -294.64 + 7.69 FG%

p value < 0.05, There is a significant relationship

b)slope is positive, increase in Win % as the FG% increases, for every 1 unit increase in FG%, there is 7.69 increase of Win%

c)

y = -407.1775 + 4.9809 X1 + 2.3651 X2 + 0.003840 X3 + 3.4224 X4 + 3.6594 X5

y^ = - 407.1775 + 4.9809 FG% + 2.3651 3P% + 0.0038 FT% + 3.4224 RBOff% + 3.6594 RBDef%

d)

Here removed X3 because its variable not significant at 0.05

Y = -406.8729 + 4.9816 X₁ + 2.3642 X₂ + 3.4199 X₄ + 3.6598 X₅

y^ = - 406.8729 + 4.9816 FG% + 2.3642 3P% + 3.4199 RBOff% + 3.6598 RBDef%

e)

FG= 45, 3P% = 35, RBOff% = 12, and RBDef = 30

Y = -406.8729 + 4.9816 X₁ + 2.3642 X₂ + 3.4199 X₄ + 3.6598 X₅

Y = -406.8729 + 4.9816 (45) + 2.3642 (35) + 3.4199 (12) + 3.6598 (30)

Y = 50.8789

Y = 50.9%