Brittany Oliva UID 003933164 Stats 101a HW7 Problem one (Chapter six: problem five on page 224) An avid fan of the PGA tour with limited background in statistics has sought your help in answering one of the age-old questions in golf, namely, what is the relative importance of each different aspect of the game on average prize money in professional golf? Y, PrizeMoney = average prize money per tournament x1, Driving Accuracy is the percent of time a player is able to hit the fairway with his tee shot. x2, GIR, Greens in Regulation is the percent of time a player was able to hit the green in regulation. A green is considered hit in regulation if any part of the ball is touching the putting surface and the number of strokes taken is two or less than par. x3, Putting Average measures putting performance on those holes where the green is hit in regulation (GIR). By using greens hit in regulation the effects of chipping close and one putting are eliminated. x4, Birdie Conversion% is the percent of time a player makes birdie or better after hitting the green in regulation. x5, SandSaves% is the percent of time a player was able to get “up and down” once in a greenside sand bunker. x6, Scrambling% is the percent of time that a player misses the green in regulation, but still makes par or better. x7, PuttsPerRound is the average total number of putts per round (a) Instead of (a), compare a model with all (un-transformed) predictors against Y, with all transformed (log(y)) predictors against Y. Which fits better and why? Un-transformed Model R Output > m1 <- lm(PrizeMoney ~ DrivingAccuracy + GIR + PuttingAverage + BirdieConversion + SandSaves + Scrambling + PuttsPerRound) Call: lm(formula = PrizeMoney ~ DrivingAccuracy + GIR + PuttingAverage + BirdieConversion + SandSaves + Scrambling + PuttsPerRound) Residuals: Min 1Q Median 3Q Max -81239 -26260 -6521 17539 420230 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -1165233.1 587382.9 -1.984 0.048737 * DrivingAccuracy -1835.8 889.2 -2.065 0.040326 * GIR 9671.3 3309.4 2.922 0.003899 ** PuttingAverage -47435.3 521566.4 -0.091 0.927631 BirdieConversion 10426.0 3049.6 3.419 0.000771 *** SandSaves 1182.1 744.8 1.587 0.114184 Scrambling 4741.3 2400.8 1.975 0.049749 * PuttsPerRound 5267.5 35765.7 0.147 0.883070 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 50140 on 188 degrees of freedom Multiple R-squared: 0.4064, Adjusted R-squared: 0.3843 F-statistic: 18.39 on 7 and 188 DF, p-value: < 2.2e-16Un-transformed Model Plots Transformed Model R Output > m1log <- lm(log(PrizeMoney) ~ log(DrivingAccuracy) + log(GIR) + log(PuttingAverage) + log(BirdieConversion) + log(SandSaves) + log(Scrambling) + log(PuttsPerRound)) Call: lm(formula = log(PrizeMoney) ~ log(DrivingAccuracy) + log(GIR) + log(PuttingAverage) + log(BirdieConversion) + log(SandSaves) + log(Scrambling) + log(PuttsPerRound)) Residuals: Min 1Q Median 3Q Max -78193 -26559 -7585 16304 437263 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -5603007 2809186 -1.995 0.04754 * log(DrivingAccuracy) -129745 57242 -2.267 0.02455 * log(GIR) 557728 217275 2.567 0.01104 * log(PuttingAverage) -567684 934916 -0.607 0.54445 log(BirdieConversion) 257970 89115 2.895 0.00424 ** log(SandSaves) 55178 36381 1.517 0.13103 log(Scrambling) 309433 139115 2.224 0.02732 * log(PuttsPerRound) 549595 1053221 0.522 0.60241 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 50970 on 188 degrees of freedom Multiple R-squared: 0.3865, Adjusted R-squared: 0.3637 F-statistic: 16.92 on 7 and 188 DF, p-value: < 2.2e-16Transformed Model Plots The un-transformed model seems to be the better fit of the two because: The un-transformed model has an R2 of .4064 as compared to the transformed model with an R2 .3865 The un-transformed has more significant predictors as compared to the transformed model Comparing all the plots from both models, there are hardly any differences between them which would lead me to choose the less complicated model of the two (b) Develop a valid full regression model containing all seven potential predictor variables listed above. Ensure that you provide justification for your choice of full model, which includes scatter plots of the data, plots of standardized residuals, and any other relevant diagnostic plots. The valid full regression model R output and plots (Same data as part a) since part a) was changed by professor): > m1 <- lm(PrizeMoney ~ DrivingAccuracy + GIR + PuttingAverage + BirdieConversion + SandSaves + Scrambling + PuttsPerRound) Call: lm(formula = PrizeMoney ~ DrivingAccuracy + GIR + PuttingAverage + BirdieConversion + SandSaves + Scrambling + PuttsPerRound) Residuals: Min 1Q Median 3Q Max -81239 -26260 -6521 17539 420230Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -1165233.1 587382.9 -1.984 0.048737 * DrivingAccuracy -1835.8 889.2 -2.065 0.040326 * GIR 9671.3 3309.4 2.922 0.003899 ** PuttingAverage -47435.3 521566.4 -0.091 0.927631 BirdieConversion 10426.0 3049.6 3.419 0.000771 *** SandSaves 1182.1 744.8 1.587 0.114184 Scrambling 4741.3 2400.8 1.975 0.049749 * PuttsPerRound 5267.5 35765.7 0.147 0.883070 Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 50140 on 188 degrees of freedom Multiple R-squared: 0.4064, Adjusted R-squared: 0.3843