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SBE10 CP16

# SBE10 CP16 - Chapter 16 Regression Analysis Model Building...

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Chapter 16 Regression Analysis: Model Building Chapter 16 Regression Analysis: Model Building Case Problem 1: PGA Tour Descriptive statistics and the sample correlation coefficients for the data follow: Variable Mean StDev Minimum Q1 Median Q3 Maximum Earnings 1632143 1325944 626736 870121 1184458 1963451 10628023 Scoring Avg. 70.885 0.513 69.110 70.550 70.940 71.145 72.320 Yards/Drive 289.87 8.72 258.70 284.35 289.60 295.10 316.10 Driving Acc. 62.802 4.850 49.300 59.850 62.400 66.050 75.900 Greens In Reg. 65.687 2.502 59.600 64.050 65.700 67.300 71.800 Putting Avg. 1.7745 0.0228 1.7100 1.7620 1.7760 1.7900 1.8370 Save Pct. 50.009 6.232 32.500 46.300 49.600 54.600 63.000 Earnings Scoring Avg. Yards/Drive Driving Acc. Scoring Avg. -0.633 0.000 Yards/Drive 0.325 -0.175 0.000 0.050 Driving Acc. -0.125 -0.124 -0.669 0.166 0.168 0.000 Greens In Re 0.367 -0.604 0.248 0.327 0.000 0.000 0.005 0.000 Putting Avg. -0.258 0.417 0.033 0.134 0.004 0.000 0.717 0.136 Save Pct. 0.161 -0.128 -0.201 -0.058 0.073 0.155 0.025 0.524 Greens In Re Putting Avg. Putting Avg. 0.223 0.012 Save Pct. -0.186 -0.173 0.037 0.054 Cell Contents: Pearson correlation P-Value We see that for the top 125 players the average earnings is \$1,632,143, the average score is 70.89, the average yards per drive is 289.9, and so on. The sample correlation coefficient between earnings and the average score is -.633; thus, lower scores are associated with higher earnings. In analyzing the data in an attempt to predict the average score, earnings would not be considered an independent variable; it is simply another output measure that has been used to rank the data. The sample correlation coefficients show that the independent variable most highly correlated with the average score is the percentage of time a player is able to hit the green in regulation. Thus, the best single variable model uses Greens In Reg. to predict Scoring Avg. The corresponding Minitab regression output is shown below: The regression equation is Scoring Avg. = 79.0 - 0.124 Greens In Reg. CP - 61

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Chapter 16 Regression Analysis: Model Building Predictor Coef SE Coef T P Constant 79.0294 0.9694 81.52 0.000 Greens In Reg. -0.12398 0.01475 -8.41 0.000 S = 0.410863 R-Sq = 36.5% R-Sq(adj) = 36.0% Analysis of Variance Source DF SS MS F P Regression 1 11.931 11.931 70.68 0.000 Residual Error 123 20.763 0.169 Total 124 32.694 The best single variable equation is able to explain 36% of the variation in the average score. To investigate what other independent variables might be useful in predicting the average score we used Minitab’s best- subsets procedure. Response is Scoring Avg. G r D e P Y r e u a i n t r v s t S d i i a s n I n v / g n g e D r A R A P i c e v c Mallows v c g g t Vars R-Sq R-Sq(adj) C-p S e . . . . 1 36.5 36.0 144.5 0.41086 X 1 17.3 16.7 224.6 0.46871 X 2 68.5 68.0 12.7 0.29058 X X 2 42.5 41.5 121.5 0.39261 X X 3 71.3 70.6 2.8 0.27825 X X X 3 68.7 67.9 14.1 0.29102 X X X 4 71.5 70.6 4.1 0.27852 X X X X 4 71.5 70.6 4.1 0.27856 X X X X 5 71.5 70.3 6.0 0.27963 X X X X X This output indicates that three independent variables (Greens In Reg., Putting Avg., and Save Pct.) can be used to develop an estimated regression equation with R-Sq (adj) = 70.6. The Minitab regression output for this model follows: The regression equation is Scoring Avg. = 59.6 - 0.156 Greens In Reg. + 12.5 Putting Avg.
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SBE10 CP16 - Chapter 16 Regression Analysis Model Building...

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