Final Project
Drew Hargis
2024-04-12
pga = read.csv('C:/Users/13175/Downloads/PgaTour5.csv',header = T)
head(pga)## Player.Name AvgScore DriveDst FrwyHit PttsperHo GreensReg AvgFin TotWin
## 1 S.Scheffler 69.02 297.9 73.54 1.668 76.13 5.11 15093235
## 2 R.McIlroy 70.68 312.2 72.05 1.744 67.87 22.14 1608505
## 3 J.Rahm 68.82 304.0 55.71 1.580 74.81 12.17 9871540
## 4 W.Clark 70.22 309.2 58.29 1.698 71.33 22.00 7951009
## 5 X.Schauffele 69.92 302.4 68.78 1.706 71.40 12.56 5284208
## 6 V.Hovland 72.10 300.4 65.19 1.725 66.96 33.00 653025summary(pga)## Player.Name AvgScore DriveDst FrwyHit
## Length:25 Min. :68.82 Min. :285.5 Min. :55.71
## Class :character 1st Qu.:70.57 1st Qu.:295.8 1st Qu.:65.19
## Mode :character Median :70.88 Median :299.5 Median :68.21
## Mean :70.79 Mean :299.1 Mean :68.33
## 3rd Qu.:71.21 3rd Qu.:302.4 3rd Qu.:72.05
## Max. :72.10 Max. :312.2 Max. :81.21
## PttsperHo GreensReg AvgFin TotWin
## Min. :1.580 Min. :63.58 Min. : 5.11 Min. : 443873
## 1st Qu.:1.705 1st Qu.:65.94 1st Qu.:22.14 1st Qu.: 2026050
## Median :1.725 Median :67.87 Median :32.83 Median : 2150141
## Mean :1.728 Mean :68.41 Mean :32.57 Mean : 3736763
## 3rd Qu.:1.753 3rd Qu.:70.00 3rd Qu.:37.40 3rd Qu.: 4492870
## Max. :1.813 Max. :76.13 Max. :62.60 Max. :15093235Regression Model Total Variables
model1 = lm(log(TotWin)~GreensReg+AvgScore+DriveDst+FrwyHit+PttsperHo+AvgFin, data = pga)
summary(model1)##
## Call:
## lm(formula = log(TotWin) ~ GreensReg + AvgScore + DriveDst +
## FrwyHit + PttsperHo + AvgFin, data = pga)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.71570 -0.22438 0.00649 0.32519 0.58231
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 59.456310 15.463629 3.845 0.00119 **
## GreensReg 0.002546 0.054005 0.047 0.96292
## AvgScore -0.534520 0.184430 -2.898 0.00958 **
## DriveDst -0.035559 0.018040 -1.971 0.06429 .
## FrwyHit -0.022341 0.021628 -1.033 0.31531
## PttsperHo 3.764253 3.008743 1.251 0.22691
## AvgFin -0.040554 0.011051 -3.670 0.00175 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4247 on 18 degrees of freedom
## Multiple R-squared: 0.8071, Adjusted R-squared: 0.7427
## F-statistic: 12.55 on 6 and 18 DF, p-value: 1.392e-05Total Winnings ~ strongest variables
model2 = lm(TotWin~GreensReg+AvgScore+AvgFin, data=pga)
summary(model2)##
## Call:
## lm(formula = TotWin ~ GreensReg + AvgScore + AvgFin, data = pga)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2707070 -1099062 144919 890511 3892950
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 113594600 54395693 2.088 0.04913 *
## GreensReg 348907 195198 1.787 0.08831 .
## AvgScore -1864448 649514 -2.871 0.00916 **
## AvgFin -53304 36590 -1.457 0.15996
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1576000 on 21 degrees of freedom
## Multiple R-squared: 0.8011, Adjusted R-squared: 0.7727
## F-statistic: 28.19 on 3 and 21 DF, p-value: 1.48e-07Quadratic Model
model3 = lm(TotWin~GreensReg+(AvgScore^2)+AvgFin, data=pga)
summary(model3)##
## Call:
## lm(formula = TotWin ~ GreensReg + (AvgScore^2) + AvgFin, data = pga)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2707070 -1099062 144919 890511 3892950
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 113594600 54395693 2.088 0.04913 *
## GreensReg 348907 195198 1.787 0.08831 .
## AvgScore -1864448 649514 -2.871 0.00916 **
## AvgFin -53304 36590 -1.457 0.15996
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1576000 on 21 degrees of freedom
## Multiple R-squared: 0.8011, Adjusted R-squared: 0.7727
## F-statistic: 28.19 on 3 and 21 DF, p-value: 1.48e-07Interaction Term
model4 = lm(TotWin~GreensReg*AvgScore+AvgFin, data=pga)
summary(model4)##
## Call:
## lm(formula = TotWin ~ GreensReg * AvgScore + AvgFin, data = pga)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2324844 -858482 87524 509094 2245499
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.353e+09 5.205e+08 -2.600 0.01714 *
## GreensReg 2.130e+07 7.406e+06 2.876 0.00934 **
## AvgScore 1.897e+07 7.386e+06 2.569 0.01831 *
## AvgFin -5.310e+04 3.168e+04 -1.676 0.10930
## GreensReg:AvgScore -2.978e+05 1.052e+05 -2.830 0.01035 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1364000 on 20 degrees of freedom
## Multiple R-squared: 0.858, Adjusted R-squared: 0.8296
## F-statistic: 30.2 on 4 and 20 DF, p-value: 3.202e-08#Answers to Step3: This model will provide the most accurate prediction, as the adjusted r-squared value is the highest.
85.8% of variation in an average pro golfer’s winnings is explained by greens in regulation*average score, and average finish.
Coefficients: - for every additional increase in the GIR statistic, the yearly average total winnings will increase by about $21 million - for every additional decrease in average score, the yearly average total winnings will increase by about $18 million - for every additional decrease in average finishm the yearly average total winnings will increase by about $53 thousand.
Scatterplot of Greens in regulation against total winnings
library(ggplot2)
attach(pga)
ggplot(data = pga, aes(x = GreensReg, y = TotWin)) +
geom_point() +
geom_smooth(method = "lm") +
labs(title = "OLS",
x = "% Greens in Reg",
y = "2024 Earnings")## `geom_smooth()` using formula = 'y ~ x'
Scatterplot of Total Average Score against total winnings
library(ggplot2)
attach(pga)## The following objects are masked from pga (pos = 3):
##
## AvgFin, AvgScore, DriveDst, FrwyHit, GreensReg, Player.Name,
## PttsperHo, TotWinggplot(data = pga, aes(x = AvgScore, y = TotWin)) +
geom_point() +
geom_smooth(method = "lm") +
labs(title = "OLS",
x = "Average Score",
y = "2024 Earnings")## `geom_smooth()` using formula = 'y ~ x'
### Regression model of average score compared against earnings
model5 = lm(TotWin~AvgFin, data = pga)
summary(model5)##
## Call:
## lm(formula = TotWin ~ AvgFin, data = pga)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4025899 -1358532 -170402 551332 6358954
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9664426 1157216 8.351 2.04e-08 ***
## AvgFin -182025 32843 -5.542 1.23e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2209000 on 23 degrees of freedom
## Multiple R-squared: 0.5718, Adjusted R-squared: 0.5532
## F-statistic: 30.72 on 1 and 23 DF, p-value: 1.228e-05pga %>%
drop_na(DriveDst) %>%
mutate(Over300 = ifelse(DriveDst >= 300,1,0)) -> pga_grpmodel6=lm(TotWin ~ Over300,data = pga_grp)
summary(model6)##
## Call:
## lm(formula = TotWin ~ Over300, data = pga_grp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3193737 -1820712 -1485083 857646 11458011
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3635225 935858 3.884 0.000749 ***
## Over300 211538 1350795 0.157 0.876925
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3374000 on 23 degrees of freedom
## Multiple R-squared: 0.001065, Adjusted R-squared: -0.04237
## F-statistic: 0.02452 on 1 and 23 DF, p-value: 0.8769result=exp(15.66)
print(result)## [1] 6324870Answers to Step 4
We chose to select Saheeth Theegala from our data set, the 16th best golfer in the world at the time our data was taken. The best model that we created was model3. By plugging the figures in by hand, we predicted that his yearly golf earnings would be 6.32 million. His actual golf earnings are 4.4 million. The percentage error between these two values is 43.6%. This percentage error could be due to a number of factors, but I would expect that this difference was mostly due to unknown factors not included in our model predicting golf earnings.