The National Basketball Association (NBA) records a variety of statistics for ea

Question

The National Basketball Association (NBA) records a variety of statistics for each team. Four of these statistics are the proportion of games won (PCT), the proportion of field goals made by the team (FG%), the proportion of three-point shots made by the team's opponent (Opp 3 Pt%), and the number of turnovers committed by the team's opponent (Opp TO). The following data show the values of these statistics for the 29 teams in the NBA for a portion of the 2004 season (NBA website, January 3, 2004). Determine the estimated regression equation that can be used to predict the proportion of games won given the proportion of field goals made by the team. Provide an interpretation for the slope of the estimated regression equation developed in part Determine the estimated regression equation that can be used to predict the proportion of games won given the proportion of field goals made by the team, the proportion of three-point shots made by the team's opponent, and the number of turnovers committed by the team's opponent. Discuss the practical implications of the estimated regression equation developed in part Estimate the proportion of games won for a team with the following values for the three independent variables: FG% =.45, Opp 3 Pt% =.34, and Opp TO = 17.

Explanation / Answer

I will use MINITAB to perform the regressions.

(a) The regression analysis gives the followng results.

Regression Analysis: PCT versus FG%

Analysis of Variance

Source         DF Adj SS   Adj MS F-Value P-Value
Regression      1 0.1146 0.11461     7.11    0.013
FG%           1 0.1146 0.11461     7.11    0.013
Error          26 0.4188 0.01611
Lack-of-Fit 20 0.3143 0.01571     0.90    0.608
Pure Error    6 0.1045 0.01742
Total          27 0.5334

Model Summary

       S      R-sq    R-sq(adj) R-sq(pred)
0.126920 21.48%     18.46%      11.39%

Coefficients

Term        Coef SE Coef T-Value P-Value   VIF
Constant -1.268    0.665    -1.91    0.068
FG%         4.08     1.53     2.67    0.013 1.00

Regression Equation

PCT = -1.268 + 4.08 FG%

(b) Since the slope is positive , there will be an increase in PCT as the value of FG% increases.For every one unit increase in FG%, we can expect an 4.08unit increase of PCT.

(c) The multiple regression analysis gives the following results.

Regression Analysis: PCT versus FG%, TO, Opp 3 Pt%

Analysis of Variance

Source       DF   Adj SS   Adj MS F-Value P-Value
Regression    3 0.27750 0.09250     8.67    0.000
FG%         1 0.14694 0.14694    13.78    0.001
TO          1 0.02861 0.02861     2.68    0.114
Opp 3 Pt%   1 0.13722 0.13722    12.87    0.001
Error        24 0.25593 0.01066
Total        27 0.53343

Model Summary

       S    R-sq R-sq(adj) R-sq(pred)
0.103266 52.02%     46.02%      36.41%

Coefficients

Term         Coef SE Coef T-Value P-Value   VIF
Constant   -0.931    0.619    -1.50    0.146
FG%          4.65     1.25     3.71    0.001 1.01
TO         0.0222   0.0135     1.64    0.114 1.00
Opp 3 Pt% -2.694    0.751    -3.59    0.001 1.01

Regression Equation

PCT = -0.931 + 4.65 FG% + 0.0222 TO - 2.694 Opp 3 Pt%

(d) The equation developed in part(c) can be used to estimate the percentages of games won, if are provided with the proportion of the field goals made by the team, proportion of three points shots made by the team's opponent, and the number of the turnovers committed by the team's opponent.

(e)

PCT = -0.931 + 4.65 *0.45 + 0.0222 *17 - 2.694 *0.34 = 0.623

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