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Intro to Linear Regression: First Base hitting stats
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# Read in data
firstbase = read.csv("firstbasestats.csv")
str(firstbase)'data.frame': 23 obs. of 15 variables:
$ Player : chr "Freddie Freeman" "Jose Abreu" "Nate Lowe" "Paul Goldschmidt" ...
$ Pos : chr "1B" "1B" "1B" "1B" ...
$ Team : chr "LAD" "CHW" "TEX" "STL" ...
$ GP : int 159 157 157 151 160 140 160 145 146 143 ...
$ AB : int 612 601 593 561 638 551 583 555 545 519 ...
$ H : int 199 183 179 178 175 152 141 139 132 124 ...
$ X2B : int 47 40 26 41 35 27 25 28 40 23 ...
$ HR : int 21 15 27 35 32 20 36 22 8 18 ...
$ RBI : int 100 75 76 115 97 84 94 85 53 63 ...
$ AVG : num 0.325 0.305 0.302 0.317 0.274 0.276 0.242 0.251 0.242 0.239 ...
$ OBP : num 0.407 0.379 0.358 0.404 0.339 0.34 0.327 0.305 0.288 0.319 ...
$ SLG : num 0.511 0.446 0.492 0.578 0.48 0.437 0.477 0.423 0.36 0.391 ...
$ OPS : num 0.918 0.824 0.851 0.981 0.818 0.777 0.804 0.729 0.647 0.71 ...
$ WAR : num 5.77 4.19 3.21 7.86 3.85 3.07 5.05 1.32 -0.33 1.87 ...
$ Payroll.Salary2023: num 27000000 19500000 4050000 26000000 14500000 ...summary(firstbase) Player Pos Team GP AB
Length:23 Length:23 Length:23 Min. : 5.0 Min. : 14.0
Class :character Class :character Class :character 1st Qu.:105.5 1st Qu.:309.0
Mode :character Mode :character Mode :character Median :131.0 Median :465.0
Mean :120.2 Mean :426.9
3rd Qu.:152.0 3rd Qu.:558.0
Max. :160.0 Max. :638.0
H X2B HR RBI AVG
Min. : 3.0 Min. : 1.00 Min. : 0.00 Min. : 1.00 Min. :0.2020
1st Qu.: 74.5 1st Qu.:13.50 1st Qu.: 8.00 1st Qu.: 27.00 1st Qu.:0.2180
Median :115.0 Median :23.00 Median :18.00 Median : 63.00 Median :0.2420
Mean :110.0 Mean :22.39 Mean :17.09 Mean : 59.43 Mean :0.2499
3rd Qu.:146.5 3rd Qu.:28.00 3rd Qu.:24.50 3rd Qu.: 84.50 3rd Qu.:0.2750
Max. :199.0 Max. :47.00 Max. :36.00 Max. :115.00 Max. :0.3250
OBP SLG OPS WAR Payroll.Salary2023
Min. :0.2140 Min. :0.2860 Min. :0.5000 Min. :-1.470 Min. : 720000
1st Qu.:0.3030 1st Qu.:0.3505 1st Qu.:0.6445 1st Qu.: 0.190 1st Qu.: 739200
Median :0.3210 Median :0.4230 Median :0.7290 Median : 1.310 Median : 4050000
Mean :0.3242 Mean :0.4106 Mean :0.7346 Mean : 1.788 Mean : 6972743
3rd Qu.:0.3395 3rd Qu.:0.4690 3rd Qu.:0.8175 3rd Qu.: 3.140 3rd Qu.: 8150000
Max. :0.4070 Max. :0.5780 Max. :0.9810 Max. : 7.860 Max. :27000000 # Linear Regression (one variable)
model1 = lm(Payroll.Salary2023 ~ RBI, data=firstbase)
summary(model1)
Call:
lm(formula = Payroll.Salary2023 ~ RBI, data = firstbase)
Residuals:
Min 1Q Median 3Q Max
-10250331 -5220790 -843455 2386848 13654950
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2363744 2866320 -0.825 0.41883
RBI 157088 42465 3.699 0.00133 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 6516000 on 21 degrees of freedom
Multiple R-squared: 0.3945, Adjusted R-squared: 0.3657
F-statistic: 13.68 on 1 and 21 DF, p-value: 0.001331# Sum of Squared Errors
model1$residuals 1 2 3 4 5 6 7
13654950.2 10082148.6 -5524939.3 10298631.2 1626214.0 -6731642.8 -5902522.2
8 9 10 11 12 13 14
-10250330.7 -4711916.8 -532796.1 -6667082.5 -6696203.1 7582148.6 -4916640.9
15 16 17 18 19 20 21
-1898125.3 -336532.3 -995042.5 -1311618.3 -843454.5 8050721.3 1250336.9
22 23
1847040.4 2926656.0 SSE = sum(model1$residuals^2)
SSE[1] 8.914926e+14# Linear Regression (two variables)
model2 = lm(Payroll.Salary2023 ~ AVG + RBI, data=firstbase)
summary(model2)
Call:
lm(formula = Payroll.Salary2023 ~ AVG + RBI, data = firstbase)
Residuals:
Min 1Q Median 3Q Max
-9097952 -4621582 -33233 3016541 10260245
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -18083756 9479037 -1.908 0.0709 .
AVG 74374031 42934155 1.732 0.0986 .
RBI 108850 49212 2.212 0.0388 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 6226000 on 20 degrees of freedom
Multiple R-squared: 0.4735, Adjusted R-squared: 0.4209
F-statistic: 8.994 on 2 and 20 DF, p-value: 0.001636# Sum of Squared Errors
SSE = sum(model2$residuals^2)
SSE[1] 7.751841e+14# Linear Regression (all variables)
model3 = lm(Payroll.Salary2023 ~ HR + RBI + AVG + OBP+ OPS, data=firstbase)
summary(model3)
Call:
lm(formula = Payroll.Salary2023 ~ HR + RBI + AVG + OBP + OPS,
data = firstbase)
Residuals:
Min 1Q Median 3Q Max
-9611440 -3338119 64016 4472451 9490309
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -31107859 11738494 -2.650 0.0168 *
HR -341069 552069 -0.618 0.5449
RBI 115786 113932 1.016 0.3237
AVG -63824769 104544645 -0.611 0.5496
OBP 27054948 131210166 0.206 0.8391
OPS 60181012 95415131 0.631 0.5366
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 6023000 on 17 degrees of freedom
Multiple R-squared: 0.5811, Adjusted R-squared: 0.4579
F-statistic: 4.717 on 5 and 17 DF, p-value: 0.006951# Sum of Squared Errors
SSE = sum(model3$residuals^2)
SSE[1] 6.167793e+14# Remove HR
model4 = lm(Payroll.Salary2023 ~ RBI + AVG + OBP+OPS, data=firstbase)
summary(model4)
Call:
lm(formula = Payroll.Salary2023 ~ RBI + AVG + OBP + OPS, data = firstbase)
Residuals:
Min 1Q Median 3Q Max
-9399551 -3573842 98921 3979339 9263512
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -29466887 11235931 -2.623 0.0173 *
RBI 71495 87015 0.822 0.4220
AVG -11035457 59192453 -0.186 0.8542
OBP 86360720 87899074 0.982 0.3389
OPS 9464546 47788458 0.198 0.8452
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 5919000 on 18 degrees of freedom
Multiple R-squared: 0.5717, Adjusted R-squared: 0.4765
F-statistic: 6.007 on 4 and 18 DF, p-value: 0.00298firstbase<-firstbase[,-(1:3)]cor(firstbase$AVG, firstbase$OBP)[1] 0.8028894cor(firstbase) GP AB H X2B HR RBI AVG
GP 1.0000000 0.9779421 0.9056508 0.8446267 0.7432552 0.8813917 0.4430808
AB 0.9779421 1.0000000 0.9516701 0.8924632 0.7721339 0.9125839 0.5126292
H 0.9056508 0.9516701 1.0000000 0.9308318 0.7155225 0.9068893 0.7393167
X2B 0.8446267 0.8924632 0.9308318 1.0000000 0.5889699 0.8485911 0.6613085
HR 0.7432552 0.7721339 0.7155225 0.5889699 1.0000000 0.8929048 0.3444242
RBI 0.8813917 0.9125839 0.9068893 0.8485911 0.8929048 1.0000000 0.5658479
AVG 0.4430808 0.5126292 0.7393167 0.6613085 0.3444242 0.5658479 1.0000000
OBP 0.4841583 0.5026125 0.6560021 0.5466537 0.4603408 0.5704463 0.8028894
SLG 0.6875270 0.7471949 0.8211406 0.7211259 0.8681501 0.8824090 0.7254274
OPS 0.6504483 0.6980141 0.8069779 0.6966830 0.7638721 0.8156612 0.7989005
WAR 0.5645243 0.6211558 0.7688712 0.6757470 0.6897677 0.7885666 0.7855945
Payroll.Salary2023 0.4614889 0.5018820 0.6249911 0.6450730 0.5317619 0.6281239 0.5871543
OBP SLG OPS WAR Payroll.Salary2023
GP 0.4841583 0.6875270 0.6504483 0.5645243 0.4614889
AB 0.5026125 0.7471949 0.6980141 0.6211558 0.5018820
H 0.6560021 0.8211406 0.8069779 0.7688712 0.6249911
X2B 0.5466537 0.7211259 0.6966830 0.6757470 0.6450730
HR 0.4603408 0.8681501 0.7638721 0.6897677 0.5317619
RBI 0.5704463 0.8824090 0.8156612 0.7885666 0.6281239
AVG 0.8028894 0.7254274 0.7989005 0.7855945 0.5871543
OBP 1.0000000 0.7617499 0.8987390 0.7766375 0.7025979
SLG 0.7617499 1.0000000 0.9686752 0.8611140 0.6974086
OPS 0.8987390 0.9686752 1.0000000 0.8799893 0.7394981
WAR 0.7766375 0.8611140 0.8799893 1.0000000 0.8086359
Payroll.Salary2023 0.7025979 0.6974086 0.7394981 0.8086359 1.0000000#Removing AVG
model5 = lm(Payroll.Salary2023 ~ RBI + OBP+OPS, data=firstbase)
summary(model5)
Call:
lm(formula = Payroll.Salary2023 ~ RBI + OBP + OPS, data = firstbase)
Residuals:
Min 1Q Median 3Q Max
-9465449 -3411234 259746 4102864 8876798
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -29737007 10855411 -2.739 0.013 *
RBI 72393 84646 0.855 0.403
OBP 82751360 83534224 0.991 0.334
OPS 7598051 45525575 0.167 0.869
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 5767000 on 19 degrees of freedom
Multiple R-squared: 0.5709, Adjusted R-squared: 0.5031
F-statistic: 8.426 on 3 and 19 DF, p-value: 0.000913model6 = lm(Payroll.Salary2023 ~ RBI + OBP, data=firstbase)
summary(model6)
Call:
lm(formula = Payroll.Salary2023 ~ RBI + OBP, data = firstbase)
Residuals:
Min 1Q Median 3Q Max
-9045497 -3487008 139497 4084739 9190185
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -28984802 9632560 -3.009 0.00693 **
RBI 84278 44634 1.888 0.07360 .
OBP 95468873 33385182 2.860 0.00969 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 5625000 on 20 degrees of freedom
Multiple R-squared: 0.5703, Adjusted R-squared: 0.5273
F-statistic: 13.27 on 2 and 20 DF, p-value: 0.0002149# Read in test set
firstbaseTest = read.csv("firstbasestats_test.csv")
str(firstbaseTest)'data.frame': 2 obs. of 15 variables:
$ Player : chr "Matt Olson" "Josh Bell"
$ Pos : chr "1B" "1B"
$ Team : chr "ATL" "SD"
$ GP : int 162 156
$ AB : int 616 552
$ H : int 148 147
$ X2B : int 44 29
$ HR : int 34 17
$ RBI : int 103 71
$ AVG : num 0.24 0.266
$ OBP : num 0.325 0.362
$ SLG : num 0.477 0.422
$ OPS : num 0.802 0.784
$ WAR : num 3.29 3.5
$ Payroll.Salary2023: num 21000000 16500000# Make test set predictions
predictTest = predict(model6, newdata=firstbaseTest)
predictTest 1 2
10723186 11558647 # Compute R-squared
SSE = sum((firstbaseTest$Payroll.Salary2023 - predictTest)^2)
SST = sum((firstbaseTest$Payroll.Salary2023 - mean(firstbase$Payroll.Salary2023))^2)
1 - SSE/SST[1] 0.5477734