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%

SUMMARY OUTPUT Regression Statistics Multiple R Square Adjusted R Square Standard Error Observations 0.733842673 0.538525068 0.522043821 10.79110525 30 ANOVA df Significance F MS Regression Residual Total 1 3804.939 3804.939 28 3260.5427 116.447952 29 7065.4817 32.67501847 3.93806E-06 Coefficients tandard Erro t Stat 294.6472391 60.322265 4.884552 7.693791616 1.3459611 5.71620665 P-value 3.80277E-05 418.2117964-171.0826818-418.2118 -171.082682 3.93806E-06 Upper 95% Lower 95.0% Upper 95.0% Lower 95% Intercept X Variable 1 4.936715385 10.45086785 4.93671539 10.45086785

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%

Y -406.8729 + 4.9816 X1 + 2.3642 X2 + 3.4199 X4 + 3.6598 X5 Correlation matrix 3 Y 1.0000 0.73380.5713-0.002010 0.011030.6674 X1 0.73381.000 0.4622 0.1137 0.2905 0.5494 X2| 0.5713 | 0.4622 | 1.000 | -0.04549 | -0.2891 | 0.2872 Xa -0.002010 0.1137 -0.04549 1.000 0.2425 0.07596 0.01103 |-0.2905|-0.2891 |-0.2425 | 1.0000 |-00890 Xy 0.6674 | 0.5494 | 0.2872 | 0.07596 | -0.08902 1.0000 ANOVA table Sum of Mean Squares Sare Statistic Source DF P-value Regression (between | 4 | 5416.2896 1354.0724 20.5263 | 1337e- i and y) Residual (between 25 1649.1921 65.9677 yi Total (between 2 7065.4817| 243.6373 yi and yi

Coefficient Table Iteration 1 (adjusted R-squared0.718) lower uppe Stand Coeff SE t-stat to.02524) o.975(24) CoeffP-value VIF b -407.1775 69.1184-5.8910 -549.8309 -264.5240 0.000 X1| 4.98091.37143.6318 2.1503 7.8114 0.000004457 0.4751 0.00 01328 1.7594 1.3556 1.0945 0.018101.2166 2.36510.8097 2.9211 0.6940 4.0362 0.33540.007480 0.003840 0.5201 0.007383 X3 -1.06971.07740.0007617 0.9942 X4 3.4224 1.34902.5370 0.63826.20660.2760 XS| 3.6594 1.29982.81530.9767 6.3421 0.33460.009582 1.4523 Coefficient Table Iteration 2 (adjusted R-squared-0.729) lower Coeff SE t-stat upper Stand CoeffSE t-stat 025(25) 0.9755) Coeff p-value VIF b-406.872954.3418 -7.4873 -518.7920 -294.9539 0.000 7.691e-8 X1 4.9816 1.3404|3.71662.2211 7.74210.47510.001022 1.7506 X2 2.3642 0.7830 3.0193 0.7515 3.97680.3353 0.005764 1.3206 X4 3.41991.27992.67210.7840 6.0559 0.27580.013081.1408 X5 3.65981.2721 2.8769 1.0398 6.2798 0.33460.008099 1.4491

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%