The Excel file Golfing Statistics provides data for a portion of the 2010 professional season for the top 25 golfers. A.) Find the best multiple regression model for predicting earnings/event as a function of the remaining variables B.) Find the best multiple regression model for predicting average score as a function of the other variables except earnings and events. Please Show VIF (Variance Inflation Factor) calculations and answer both questions in Excel Golfing Statistics Earnings/Event Events $239,493.68 22 $177,249.18 28 $218,619.18 22 $186,380.08 24 $209,511.75 20 $181,987.29 21 $162,536.13 23 $174,534.95 21 $135,353.70 27 $212,540.82 17 $297,079.50 12 $168,904.45 20 $135,791.58 24 $133,695.52 23 $112,192.04 26 $215,121.67 12 $183,922.93 14 $150,251.76 17 $183,356.69 13 $130,274.35 17 $286,285.40 5 $72,708.05 19 $99,597.31 13 $85,557.56 9 $46,406.25 8 *GIR: Greens in Regulation Avg. Score GIR (%)* Driving Distance Driving Accuracy (%) 70.37 67.9 288.4 60.2 69.43 69.4 286.9 67.9 70.23 67.1 276.0 71.0 70.46 68.0 308.5 56.4 69.78 68.3 282.9 68.5 70.34 65.1 299.1 52.7 69.92 66.3 287.8 65.2 70.25 65.3 277.0 62.4 70.64 68.0 291.8 67.9 69.93 68.7 294.2 61.3 70.26 69.3 298.7 61.3 69.96 66.0 291.4 64.8 70.21 68.5 309.8 55.7 70.53 68.2 289.1 64.8 70.59 66.5 279.7 71.2 70.22 66.5 292.4 60.1 70.86 62.9 287.2 52.0 70.94 66.2 300.0 62.6 71.13 66.9 291.7 67.1 71.53 62.5 286.8 62.7 69.73 69.4 308.4 70.6 70.79 61.9 292.1 56.7 71.07 64.1 295.8 57.2 71.10 64.1 290.4 69.3 71.24 61.1 289.9 65.5 Putts/Round 31.82 31.30 31.81 31.81 31.43 31.72 31.68 31.52 32.35 31.55 32.31 31.79 31.73 31.86 31.30 32.29 31.99 32.31 32.06 32.47 32.09 31.50 31.52 31.95 32.31 Golfing Statistics Earnings/Event $239,493.68 22 Events Avg. Score 70.37 GIR (%)* 67.9 Driving Distance 288.4 Driving Accuracy (%) 60.2 Putts/Round 31.82 GIR (%)* 67.9 $177,249.18 28 69.43 69.4 286.9 67.9 31.30 69.4 $218,619.18 22 70.23 67.1 276.0 71.0 31.81 67.1 $186,380.08 24 70.46 68.0 308.5 56.4 31.81 68.0 $209,511.75 20 69.78 68.3 282.9 68.5 31.43 68.3 $181,987.29 $162,536.13 $174,534.95 $135,353.70 $212,540.82 $297,079.50 $168,904.45 $135,791.58 $133,695.52 $112,192.04 $215,121.67 $183,922.93 $150,251.76 $183,356.69 $130,274.35 $286,285.40 $72,708.05 $99,597.31 $85,557.56 $46,406.25 21 23 21 27 17 12 20 24 23 26 12 14 17 13 17 5 19 13 9 8 70.34 69.92 70.25 70.64 69.93 70.26 69.96 70.21 70.53 70.59 70.22 70.86 70.94 71.13 71.53 69.73 70.79 71.07 71.10 71.24 65.1 66.3 65.3 68.0 68.7 69.3 66.0 68.5 68.2 66.5 66.5 62.9 66.2 66.9 62.5 69.4 61.9 64.1 64.1 61.1 299.1 287.8 277.0 291.8 294.2 298.7 291.4 309.8 289.1 279.7 292.4 287.2 300.0 291.7 286.8 308.4 292.1 295.8 290.4 289.9 52.7 65.2 62.4 67.9 61.3 61.3 64.8 55.7 64.8 71.2 60.1 52.0 62.6 67.1 62.7 70.6 56.7 57.2 69.3 65.5 31.72 31.68 31.52 32.35 31.55 32.31 31.79 31.73 31.86 31.30 32.29 31.99 32.31 32.06 32.47 32.09 31.50 31.52 31.95 32.31 65.1 66.3 65.3 68.0 68.7 69.3 66.0 68.5 68.2 66.5 66.5 62.9 66.2 66.9 62.5 69.4 61.9 64.1 64.1 61.1 *GIR: Greens in Regulation SUMMARY OUTPUT Regression Statistics Multiple R 0.9074243495 R Square 0.82341895 Adjusted R Square 0.7645586 Standard Error 29533.224333 Observations 25 From the multiple regression output the linear equation is: ANOVA Calculation of variance inflation factor df Regression Residual Total Intercept Events Average Score GIR(%) Driving distance Driving Accuracy Putts/Round Earnings = -4751.822(Events) - 44490.89(Average score) + 22563.98(GIR) - 3466.13(Driving distance) - 5463.83(Driving accuracy) + 57686.85(Putts/round) This equation gives earnings in terms of other variables with 82.34% accuracy. SS MS F Significance F 6 73210099370 1.2E+010 13.98937 6.496624E-006 18 15699804111.15 8.7E+008 24 88909903481.18 Coefficients 1411171.3952 -4751.822168 -44490.89731 22563.989222 -3466.134358 -5463.836689 57686.857552 Standard Error 1350234.637203 1288.785632619 19562.24688963 4727.341802309 999.316198827 1453.581840063 23583.59681407 t Stat 1.04513 -3.68705 -2.27432 4.773082 -3.46851 -3.75888 2.446059 P-value Lower 95% Upper 95% 0.309796 -1425566.309 4247909.0994 0.001687 -7459.460304 -2044.184031 0.035418 -85589.652895 -3392.141733 0.000152 12632.2126534 32495.76579 0.002742 -5565.619782 -1366.648934 0.001437 -8517.6988092 -2409.974569 0.024946 8139.5592966 107234.15581 VIF j S x j 2 n 1 SEb j 2 S2 S x j S tan dard deviation SEb j s tan dard error of slope coeffiecient S mean square of residuals Variable Standard deviation VIF Events 6.1746794789 1.669923 Average Score 0.5281925154 2.815322 GIR(%) 2.4189476362 3.448205 Driving distance 8.8360530404 2.056026 Driving Accuracy 5.6349014188 1.769122 Here since the p-value is less than 0.05 for all the independent variables.Hence this is the best multiple lineae regressionPutts/Round model. 0.3458436641 1.754227 SUMMARY OUTPUT Regression Statistics Multiple R 0.8060591298 R Square 0.6497313207 Adjusted R Square 0.5796775848 Standard Error 0.3424392351 Observations 25 From the multiple regression output the linear equation is: Average score=62.23 -0.15(GIR) +0.003(Driving distance)+.004(Driving accuracy) + .529(Putts/round) This equation gives average scorein terms of other variables except earnings and events with 64.97% accuracy. Calculation of variance inflation factor ANOVA df Regression Residual Total Intercept GIR(%) Driving distance Driving Accuracy Putts/Round 4 20 24 SS MS F Significance F 4.3504034049 1.087601 9.274756 0.0002084101 2.3452925951 0.117265 6.695696 Coefficients Standard Error t Stat 62.235581476 7.1277550306 8.731442 -0.1510276451 0.0357494384 -4.224616 0.0036633046 0.01061111 0.345233 0.0047269791 0.0159051075 0.297199 0.5296599042 0.2259779431 2.343857 P-value 2.9E-008 0.000416 0.733524 0.76938 0.029527 Lower 95% Upper 95% 47.3673450638 77.103817889 -0.2255996666 -0.0764556236 -0.0184710829 0.025797692 -0.0284504937 0.0379044519 0.0582781763 1.001041632 Here the p-value is less than 0.05 only for GIR and Putts/rounds.So let us again run the regression for these independent variables. SUMMARY OUTPUT Regression Statistics Multiple R 0.8046066677 R Square 0.6473918898 Adjusted R Square 0.615336607 Standard Error 0.3275915357 Observations 25 ANOVA df Regression Residual Total Intercept GIR(%) Putts/Round 2 22 24 SS MS F Significance F 4.3347392867 2.16737 20.19611 1.047648E-005 2.3609567133 0.107316 6.695696 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% 62.025593023 6.7961714356 9.126549 6.2E-009 47.9311961835 76.119989863 0.5636779424 0.1959456426 2.876706 0.008761 0.1573115533 0.9700443315 -0.1435923658 0.0280148929 -5.125573 3.9E-005 -0.2016916974 -0.0854930341 Now the p-values are less than 0.05 VIF j S x j 2 n 1 SEb j 2 S2 S x j S tan dard deviation SEb j s tan dard error of slope coeffiecient S mean square of residuals Variable GIR(%) Driving distance Driving Accuracy Putts/Round Standard deviation VIF 2.4189476362 12.50792 8.8360530404 14.70388 5.6349014188 13.43506 0.3458436641 10.21611 Golfing Statistics Earnings/Event $239,493.68 22 Events Avg. Score 70.37 GIR (%)* 67.9 Driving Distance 288.4 Driving Accuracy (%) 60.2 Putts/Round 31.82 GIR (%)* 67.9 $177,249.18 28 69.43 69.4 286.9 67.9 31.30 69.4 $218,619.18 22 70.23 67.1 276.0 71.0 31.81 67.1 $186,380.08 24 70.46 68.0 308.5 56.4 31.81 68.0 $209,511.75 20 69.78 68.3 282.9 68.5 31.43 68.3 $181,987.29 $162,536.13 $174,534.95 $135,353.70 $212,540.82 $297,079.50 $168,904.45 $135,791.58 $133,695.52 $112,192.04 $215,121.67 $183,922.93 $150,251.76 $183,356.69 $130,274.35 $286,285.40 $72,708.05 $99,597.31 $85,557.56 $46,406.25 21 23 21 27 17 12 20 24 23 26 12 14 17 13 17 5 19 13 9 8 70.34 69.92 70.25 70.64 69.93 70.26 69.96 70.21 70.53 70.59 70.22 70.86 70.94 71.13 71.53 69.73 70.79 71.07 71.10 71.24 65.1 66.3 65.3 68.0 68.7 69.3 66.0 68.5 68.2 66.5 66.5 62.9 66.2 66.9 62.5 69.4 61.9 64.1 64.1 61.1 299.1 287.8 277.0 291.8 294.2 298.7 291.4 309.8 289.1 279.7 292.4 287.2 300.0 291.7 286.8 308.4 292.1 295.8 290.4 289.9 52.7 65.2 62.4 67.9 61.3 61.3 64.8 55.7 64.8 71.2 60.1 52.0 62.6 67.1 62.7 70.6 56.7 57.2 69.3 65.5 31.72 31.68 31.52 32.35 31.55 32.31 31.79 31.73 31.86 31.30 32.29 31.99 32.31 32.06 32.47 32.09 31.50 31.52 31.95 32.31 65.1 66.3 65.3 68.0 68.7 69.3 66.0 68.5 68.2 66.5 66.5 62.9 66.2 66.9 62.5 69.4 61.9 64.1 64.1 61.1 *GIR: Greens in Regulation SUMMARY OUTPUT Regression Statistics Multiple R 0.9074243495 R Square 0.82341895 Adjusted R Square 0.7645586 Standard Error 29533.224333 Observations 25 From the multiple regression output the linear equation is: ANOVA Calculation of variance inflation factor df Regression Residual Total Intercept Events Average Score GIR(%) Driving distance Driving Accuracy Putts/Round Earnings = -4751.822(Events) - 44490.89(Average score) + 22563.98(GIR) - 3466.13(Driving distance) - 5463.83(Driving accuracy) + 57686.85(Putts/round) This equation gives earnings in terms of other variables with 82.34% accuracy. SS MS F Significance F 6 73210099370 1.2E+010 13.98937 6.496624E-006 18 15699804111.15 8.7E+008 24 88909903481.18 Coefficients 1411171.3952 -4751.822168 -44490.89731 22563.989222 -3466.134358 -5463.836689 57686.857552 Standard Error 1350234.637203 1288.785632619 19562.24688963 4727.341802309 999.316198827 1453.581840063 23583.59681407 t Stat 1.04513 -3.68705 -2.27432 4.773082 -3.46851 -3.75888 2.446059 P-value Lower 95% Upper 95% 0.309796 -1425566.309 4247909.0994 0.001687 -7459.460304 -2044.184031 0.035418 -85589.652895 -3392.141733 0.000152 12632.2126534 32495.76579 0.002742 -5565.619782 -1366.648934 0.001437 -8517.6988092 -2409.974569 0.024946 8139.5592966 107234.15581 VIF j S x j 2 n 1 SEb j 2 S2 S x j S tan dard deviation SEb j s tan dard error of slope coeffiecient S mean square of residuals Variable Standard deviation VIF Events 6.1746794789 1.669923 Average Score 0.5281925154 2.815322 GIR(%) 2.4189476362 3.448205 Driving distance 8.8360530404 2.056026 Driving Accuracy 5.6349014188 1.769122 Here since the p-value is less than 0.05 for all the independent variables.Hence this is the best multiple lineae regressionPutts/Round model. 0.3458436641 1.754227 SUMMARY OUTPUT Regression Statistics Multiple R 0.8060591298 R Square 0.6497313207 Adjusted R Square 0.5796775848 Standard Error 0.3424392351 Observations 25 From the multiple regression output the linear equation is: Average score=62.23 -0.15(GIR) +0.003(Driving distance)+.004(Driving accuracy) + .529(Putts/round) This equation gives average scorein terms of other variables except earnings and events with 64.97% accuracy. Calculation of variance inflation factor ANOVA df Regression Residual Total Intercept GIR(%) Driving distance Driving Accuracy Putts/Round 4 20 24 SS MS F Significance F 4.3504034049 1.087601 9.274756 0.0002084101 2.3452925951 0.117265 6.695696 Coefficients Standard Error t Stat 62.235581476 7.1277550306 8.731442 -0.1510276451 0.0357494384 -4.224616 0.0036633046 0.01061111 0.345233 0.0047269791 0.0159051075 0.297199 0.5296599042 0.2259779431 2.343857 P-value 2.9E-008 0.000416 0.733524 0.76938 0.029527 Lower 95% Upper 95% 47.3673450638 77.103817889 -0.2255996666 -0.0764556236 -0.0184710829 0.025797692 -0.0284504937 0.0379044519 0.0582781763 1.001041632 Here the p-value is less than 0.05 only for GIR and Putts/rounds.So let us again run the regression for these independent variables. SUMMARY OUTPUT Regression Statistics Multiple R 0.8046066677 R Square 0.6473918898 Adjusted R Square 0.615336607 Standard Error 0.3275915357 Observations 25 ANOVA df Regression Residual Total Intercept GIR(%) Putts/Round 2 22 24 SS MS F Significance F 4.3347392867 2.16737 20.19611 1.047648E-005 2.3609567133 0.107316 6.695696 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% 62.025593023 6.7961714356 9.126549 6.2E-009 47.9311961835 76.119989863 0.5636779424 0.1959456426 2.876706 0.008761 0.1573115533 0.9700443315 -0.1435923658 0.0280148929 -5.125573 3.9E-005 -0.2016916974 -0.0854930341 Now the p-values are less than 0.05 VIF j S x j 2 n 1 SEb j 2 S2 S x j S tan dard deviation SEb j s tan dard error of slope coeffiecient S mean square of residuals Variable GIR(%) Driving distance Driving Accuracy Putts/Round Standard deviation VIF 2.4189476362 12.50792 8.8360530404 14.70388 5.6349014188 13.43506 0.3458436641 10.21611 Golfing Statistics Earnings/Event $239,493.68 22 Events Avg. Score 70.37 GIR (%)* 67.9 Driving Distance 288.4 Driving Accuracy (%) 60.2 Putts/Round 31.82 GIR (%)* 67.9 $177,249.18 28 69.43 69.4 286.9 67.9 31.30 69.4 $218,619.18 22 70.23 67.1 276.0 71.0 31.81 67.1 $186,380.08 24 70.46 68.0 308.5 56.4 31.81 68.0 $209,511.75 20 69.78 68.3 282.9 68.5 31.43 68.3 $181,987.29 $162,536.13 $174,534.95 $135,353.70 $212,540.82 $297,079.50 $168,904.45 $135,791.58 $133,695.52 $112,192.04 $215,121.67 $183,922.93 $150,251.76 $183,356.69 $130,274.35 $286,285.40 $72,708.05 $99,597.31 $85,557.56 $46,406.25 21 23 21 27 17 12 20 24 23 26 12 14 17 13 17 5 19 13 9 8 70.34 69.92 70.25 70.64 69.93 70.26 69.96 70.21 70.53 70.59 70.22 70.86 70.94 71.13 71.53 69.73 70.79 71.07 71.10 71.24 65.1 66.3 65.3 68.0 68.7 69.3 66.0 68.5 68.2 66.5 66.5 62.9 66.2 66.9 62.5 69.4 61.9 64.1 64.1 61.1 299.1 287.8 277.0 291.8 294.2 298.7 291.4 309.8 289.1 279.7 292.4 287.2 300.0 291.7 286.8 308.4 292.1 295.8 290.4 289.9 52.7 65.2 62.4 67.9 61.3 61.3 64.8 55.7 64.8 71.2 60.1 52.0 62.6 67.1 62.7 70.6 56.7 57.2 69.3 65.5 31.72 31.68 31.52 32.35 31.55 32.31 31.79 31.73 31.86 31.30 32.29 31.99 32.31 32.06 32.47 32.09 31.50 31.52 31.95 32.31 65.1 66.3 65.3 68.0 68.7 69.3 66.0 68.5 68.2 66.5 66.5 62.9 66.2 66.9 62.5 69.4 61.9 64.1 64.1 61.1 *GIR: Greens in Regulation SUMMARY OUTPUT Regression Statistics Multiple R 0.9074243495 R Square 0.82341895 Adjusted R Square 0.7645586 Standard Error 29533.224333 Observations 25 From the multiple regression output the linear equation is: ANOVA Calculation of variance inflation factor df Regression Residual Total Intercept Events Average Score GIR(%) Driving distance Driving Accuracy Putts/Round Earnings = -4751.822(Events) - 44490.89(Average score) + 22563.98(GIR) - 3466.13(Driving distance) - 5463.83(Driving accuracy) + 57686.85(Putts/round) This equation gives earnings in terms of other variables with 82.34% accuracy. SS MS F Significance F 6 73210099370 1.2E+010 13.98937 6.496624E-006 18 15699804111.15 8.7E+008 24 88909903481.18 Coefficients 1411171.3952 -4751.822168 -44490.89731 22563.989222 -3466.134358 -5463.836689 57686.857552 Standard Error 1350234.637203 1288.785632619 19562.24688963 4727.341802309 999.316198827 1453.581840063 23583.59681407 t Stat 1.04513 -3.68705 -2.27432 4.773082 -3.46851 -3.75888 2.446059 P-value Lower 95% Upper 95% 0.309796 -1425566.309 4247909.0994 0.001687 -7459.460304 -2044.184031 0.035418 -85589.652895 -3392.141733 0.000152 12632.2126534 32495.76579 0.002742 -5565.619782 -1366.648934 0.001437 -8517.6988092 -2409.974569 0.024946 8139.5592966 107234.15581 VIF j S x j 2 n 1 SEb j 2 S2 S x j S tan dard deviation SEb j s tan dard error of slope coeffiecient S mean square of residuals Variable Standard deviation VIF Events 6.1746794789 1.669923 Average Score 0.5281925154 2.815322 GIR(%) 2.4189476362 3.448205 Driving distance 8.8360530404 2.056026 Driving Accuracy 5.6349014188 1.769122 Here since the p-value is less than 0.05 for all the independent variables.Hence this is the best multiple lineae regressionPutts/Round model. 0.3458436641 1.754227 SUMMARY OUTPUT Regression Statistics Multiple R 0.8060591298 R Square 0.6497313207 Adjusted R Square 0.5796775848 Standard Error 0.3424392351 Observations 25 From the multiple regression output the linear equation is: Average score=62.23 -0.15(GIR) +0.003(Driving distance)+.004(Driving accuracy) + .529(Putts/round) This equation gives average scorein terms of other variables except earnings and events with 64.97% accuracy. Calculation of variance inflation factor ANOVA df Regression Residual Total Intercept GIR(%) Driving distance Driving Accuracy Putts/Round 4 20 24 SS MS F Significance F 4.3504034049 1.087601 9.274756 0.0002084101 2.3452925951 0.117265 6.695696 Coefficients Standard Error t Stat 62.235581476 7.1277550306 8.731442 -0.1510276451 0.0357494384 -4.224616 0.0036633046 0.01061111 0.345233 0.0047269791 0.0159051075 0.297199 0.5296599042 0.2259779431 2.343857 P-value 2.9E-008 0.000416 0.733524 0.76938 0.029527 Lower 95% Upper 95% 47.3673450638 77.103817889 -0.2255996666 -0.0764556236 -0.0184710829 0.025797692 -0.0284504937 0.0379044519 0.0582781763 1.001041632 Here the p-value is less than 0.05 only for GIR and Putts/rounds.So let us again run the regression for these independent variables. SUMMARY OUTPUT Regression Statistics Multiple R 0.8046066677 R Square 0.6473918898 Adjusted R Square 0.615336607 Standard Error 0.3275915357 Observations 25 ANOVA df Regression Residual Total Intercept GIR(%) Putts/Round 2 22 24 SS MS F Significance F 4.3347392867 2.16737 20.19611 1.047648E-005 2.3609567133 0.107316 6.695696 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% 62.025593023 6.7961714356 9.126549 6.2E-009 47.9311961835 76.119989863 0.5636779424 0.1959456426 2.876706 0.008761 0.1573115533 0.9700443315 -0.1435923658 0.0280148929 -5.125573 3.9E-005 -0.2016916974 -0.0854930341 Now the p-values are less than 0.05 VIF j S x j 2 n 1 SEb j 2 S2 S x j S tan dard deviation SEb j s tan dard error of slope coeffiecient S mean square of residuals Variable GIR(%) Driving distance Driving Accuracy Putts/Round Standard deviation VIF 2.4189476362 12.50792 8.8360530404 14.70388 5.6349014188 13.43506 0.3458436641 10.21611 Golfing Statistics Earnings/Event $239,493.68 22 Events Avg. Score 70.37 GIR (%)* 67.9 Driving Distance 288.4 Driving Accuracy (%) 60.2 Putts/Round 31.82 GIR (%)* 67.9 $177,249.18 28 69.43 69.4 286.9 67.9 31.30 69.4 $218,619.18 22 70.23 67.1 276.0 71.0 31.81 67.1 $186,380.08 24 70.46 68.0 308.5 56.4 31.81 68.0 $209,511.75 20 69.78 68.3 282.9 68.5 31.43 68.3 $181,987.29 $162,536.13 $174,534.95 $135,353.70 $212,540.82 $297,079.50 $168,904.45 $135,791.58 $133,695.52 $112,192.04 $215,121.67 $183,922.93 $150,251.76 $183,356.69 $130,274.35 $286,285.40 $72,708.05 $99,597.31 $85,557.56 $46,406.25 21 23 21 27 17 12 20 24 23 26 12 14 17 13 17 5 19 13 9 8 70.34 69.92 70.25 70.64 69.93 70.26 69.96 70.21 70.53 70.59 70.22 70.86 70.94 71.13 71.53 69.73 70.79 71.07 71.10 71.24 65.1 66.3 65.3 68.0 68.7 69.3 66.0 68.5 68.2 66.5 66.5 62.9 66.2 66.9 62.5 69.4 61.9 64.1 64.1 61.1 299.1 287.8 277.0 291.8 294.2 298.7 291.4 309.8 289.1 279.7 292.4 287.2 300.0 291.7 286.8 308.4 292.1 295.8 290.4 289.9 52.7 65.2 62.4 67.9 61.3 61.3 64.8 55.7 64.8 71.2 60.1 52.0 62.6 67.1 62.7 70.6 56.7 57.2 69.3 65.5 31.72 31.68 31.52 32.35 31.55 32.31 31.79 31.73 31.86 31.30 32.29 31.99 32.31 32.06 32.47 32.09 31.50 31.52 31.95 32.31 65.1 66.3 65.3 68.0 68.7 69.3 66.0 68.5 68.2 66.5 66.5 62.9 66.2 66.9 62.5 69.4 61.9 64.1 64.1 61.1 *GIR: Greens in Regulation SUMMARY OUTPUT Regression Statistics Multiple R 0.9074243495 R Square 0.82341895 Adjusted R Square 0.7645586 Standard Error 29533.224333 Observations 25 From the multiple regression output the linear equation is: ANOVA Calculation of variance inflation factor df Regression Residual Total Intercept Events Average Score GIR(%) Driving distance Driving Accuracy Putts/Round Earnings = -4751.822(Events) - 44490.89(Average score) + 22563.98(GIR) - 3466.13(Driving distance) - 5463.83(Driving accuracy) + 57686.85(Putts/round) This equation gives earnings in terms of other variables with 82.34% accuracy. SS MS F Significance F 6 73210099370 1.2E+010 13.98937 6.496624E-006 18 15699804111.15 8.7E+008 24 88909903481.18 Coefficients 1411171.3952 -4751.822168 -44490.89731 22563.989222 -3466.134358 -5463.836689 57686.857552 Standard Error 1350234.637203 1288.785632619 19562.24688963 4727.341802309 999.316198827 1453.581840063 23583.59681407 t Stat 1.04513 -3.68705 -2.27432 4.773082 -3.46851 -3.75888 2.446059 P-value Lower 95% Upper 95% 0.309796 -1425566.309 4247909.0994 0.001687 -7459.460304 -2044.184031 0.035418 -85589.652895 -3392.141733 0.000152 12632.2126534 32495.76579 0.002742 -5565.619782 -1366.648934 0.001437 -8517.6988092 -2409.974569 0.024946 8139.5592966 107234.15581 VIF j S x j 2 n 1 SEb j 2 S2 S x j S tan dard deviation SEb j s tan dard error of slope coeffiecient S mean square of residuals Variable Standard deviation VIF Events 6.1746794789 1.669923 Average Score 0.5281925154 2.815322 GIR(%) 2.4189476362 3.448205 Driving distance 8.8360530404 2.056026 Driving Accuracy 5.6349014188 1.769122 Here since the p-value is less than 0.05 for all the independent variables.Hence this is the best multiple lineae regressionPutts/Round model. 0.3458436641 1.754227 SUMMARY OUTPUT Regression Statistics Multiple R 0.8060591298 R Square 0.6497313207 Adjusted R Square 0.5796775848 Standard Error 0.3424392351 Observations 25 From the multiple regression output the linear equation is: Average score=62.23 -0.15(GIR) +0.003(Driving distance)+.004(Driving accuracy) + .529(Putts/round) This equation gives average scorein terms of other variables except earnings and events with 64.97% accuracy. Calculation of variance inflation factor ANOVA df Regression Residual Total Intercept GIR(%) Driving distance Driving Accuracy Putts/Round 4 20 24 SS MS F Significance F 4.3504034049 1.087601 9.274756 0.0002084101 2.3452925951 0.117265 6.695696 Coefficients Standard Error t Stat 62.235581476 7.1277550306 8.731442 -0.1510276451 0.0357494384 -4.224616 0.0036633046 0.01061111 0.345233 0.0047269791 0.0159051075 0.297199 0.5296599042 0.2259779431 2.343857 P-value 2.9E-008 0.000416 0.733524 0.76938 0.029527 Lower 95% Upper 95% 47.3673450638 77.103817889 -0.2255996666 -0.0764556236 -0.0184710829 0.025797692 -0.0284504937 0.0379044519 0.0582781763 1.001041632 Here the p-value is less than 0.05 only for GIR and Putts/rounds.So let us again run the regression for these independent variables. SUMMARY OUTPUT Regression Statistics Multiple R 0.8046066677 R Square 0.6473918898 Adjusted R Square 0.615336607 Standard Error 0.3275915357 Observations 25 ANOVA df Regression Residual Total Intercept GIR(%) Putts/Round 2 22 24 SS MS F Significance F 4.3347392867 2.16737 20.19611 1.047648E-005 2.3609567133 0.107316 6.695696 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% 62.025593023 6.7961714356 9.126549 6.2E-009 47.9311961835 76.119989863 0.5636779424 0.1959456426 2.876706 0.008761 0.1573115533 0.9700443315 -0.1435923658 0.0280148929 -5.125573 3.9E-005 -0.2016916974 -0.0854930341 Now the p-values are less than 0.05 VIF j S x j 2 n 1 SEb j 2 S2 S x j S tan dard deviation SEb j s tan dard error of slope coeffiecient S mean square of residuals Variable GIR(%) Driving distance Driving Accuracy Putts/Round Standard deviation VIF 2.4189476362 12.50792 8.8360530404 14.70388 5.6349014188 13.43506 0.3458436641 10.21611