This is an R Markdown Notebook. When you execute code within the notebook, the results appear beneath the code.
Try executing this chunk by clicking the Run button within the chunk or by placing your cursor inside it and pressing Ctrl+Shift+Enter.
** Intro to Linear Regression: First Base hitting stats**
# Read in data
firstbase = read.csv("C:/Users/duway/Downloads/firstbasestats.csv")
str(firstbase)# check the structure of the data'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 ...# 23 rows and 15 columns(23 observations and 15 variables)
# create a summary of the data
summary(firstbase) Player Pos
Length:23 Length:23
Class :character Class :character
Mode :character Mode :character
Team GP AB
Length:23 Min. : 5.0 Min. : 14.0
Class :character 1st Qu.:105.5 1st Qu.:309.0
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
Min. : 3.0 Min. : 1.00 Min. : 0.00
1st Qu.: 74.5 1st Qu.:13.50 1st Qu.: 8.00
Median :115.0 Median :23.00 Median :18.00
Mean :110.0 Mean :22.39 Mean :17.09
3rd Qu.:146.5 3rd Qu.:28.00 3rd Qu.:24.50
Max. :199.0 Max. :47.00 Max. :36.00
RBI AVG OBP
Min. : 1.00 Min. :0.2020 Min. :0.2140
1st Qu.: 27.00 1st Qu.:0.2180 1st Qu.:0.3030
Median : 63.00 Median :0.2420 Median :0.3210
Mean : 59.43 Mean :0.2499 Mean :0.3242
3rd Qu.: 84.50 3rd Qu.:0.2750 3rd Qu.:0.3395
Max. :115.00 Max. :0.3250 Max. :0.4070
SLG OPS WAR
Min. :0.2860 Min. :0.5000 Min. :-1.470
1st Qu.:0.3505 1st Qu.:0.6445 1st Qu.: 0.190
Median :0.4230 Median :0.7290 Median : 1.310
Mean :0.4106 Mean :0.7346 Mean : 1.788
3rd Qu.:0.4690 3rd Qu.:0.8175 3rd Qu.: 3.140
Max. :0.5780 Max. :0.9810 Max. : 7.860
Payroll.Salary2023
Min. : 720000
1st Qu.: 739200
Median : 4050000
Mean : 6972743
3rd Qu.: 8150000
Max. :27000000 ** Create a linear model to predict HRs from ABs**
# create a linear model to predict salaries and RBI
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$residuals 1 2 3 4
13654950.2 10082148.6 -5524939.3 10298631.2
5 6 7 8
1626214.0 -6731642.8 -5902522.2 -10250330.7
9 10 11 12
-4711916.8 -532796.1 -6667082.5 -6696203.1
13 14 15 16
7582148.6 -4916640.9 -1898125.3 -336532.3
17 18 19 20
-995042.5 -1311618.3 -843454.5 8050721.3
21 22 23
1250336.9 1847040.4 2926656.0 # sse
# adj r square explains the proportion of the variance in the dependent variable that is predictable from the independent variable
# example 0.5 means 50% of the variance in the dependent variable is predictable from the independent variable
sum(model1$residuals^2)[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$residuals^2)
SSE[1] 7.751841e+14** Create a linear model to predict HRs with all predictors **
#Linear Regression (all variables)
model3 = lm(Payroll.Salary2023 ~ HR + RBI + AVG + OBP+ OPS, data=firstbase)
summary(model3)
Call:
lm(formula = Payroll.Salary2023 ~ HR + RBI + AVG + OBP + OPS,
data = firstbase)
Residuals:
Min 1Q Median 3Q Max
-9611440 -3338119 64016 4472451 9490309
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -31107859 11738494 -2.650 0.0168 *
HR -341069 552069 -0.618 0.5449
RBI 115786 113932 1.016 0.3237
AVG -63824769 104544645 -0.611 0.5496
OBP 27054948 131210166 0.206 0.8391
OPS 60181012 95415131 0.631 0.5366
---
Signif. codes:
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 6023000 on 17 degrees of freedom
Multiple R-squared: 0.5811, Adjusted R-squared: 0.4579
F-statistic: 4.717 on 5 and 17 DF, p-value: 0.006951# Sum of Squared Errors
SSE = sum(model3$residuals^2)
SSE[1] 6.167793e+14firstbase<-firstbase[,-(1:3)]# remove the first three columns# Correlations
cor(firstbase$RBI, firstbase$Payroll.Salary2023)[1] 0.6281239cor(firstbase$AVG, firstbase$OBP)[1] 0.8028894cor(firstbase)# correlation matrix GP AB H X2B
GP 1.0000000 0.9779421 0.9056508 0.8446267
AB 0.9779421 1.0000000 0.9516701 0.8924632
H 0.9056508 0.9516701 1.0000000 0.9308318
X2B 0.8446267 0.8924632 0.9308318 1.0000000
HR 0.7432552 0.7721339 0.7155225 0.5889699
RBI 0.8813917 0.9125839 0.9068893 0.8485911
AVG 0.4430808 0.5126292 0.7393167 0.6613085
OBP 0.4841583 0.5026125 0.6560021 0.5466537
SLG 0.6875270 0.7471949 0.8211406 0.7211259
OPS 0.6504483 0.6980141 0.8069779 0.6966830
WAR 0.5645243 0.6211558 0.7688712 0.6757470
Payroll.Salary2023 0.4614889 0.5018820 0.6249911 0.6450730
HR RBI AVG OBP
GP 0.7432552 0.8813917 0.4430808 0.4841583
AB 0.7721339 0.9125839 0.5126292 0.5026125
H 0.7155225 0.9068893 0.7393167 0.6560021
X2B 0.5889699 0.8485911 0.6613085 0.5466537
HR 1.0000000 0.8929048 0.3444242 0.4603408
RBI 0.8929048 1.0000000 0.5658479 0.5704463
AVG 0.3444242 0.5658479 1.0000000 0.8028894
OBP 0.4603408 0.5704463 0.8028894 1.0000000
SLG 0.8681501 0.8824090 0.7254274 0.7617499
OPS 0.7638721 0.8156612 0.7989005 0.8987390
WAR 0.6897677 0.7885666 0.7855945 0.7766375
Payroll.Salary2023 0.5317619 0.6281239 0.5871543 0.7025979
SLG OPS WAR Payroll.Salary2023
GP 0.6875270 0.6504483 0.5645243 0.4614889
AB 0.7471949 0.6980141 0.6211558 0.5018820
H 0.8211406 0.8069779 0.7688712 0.6249911
X2B 0.7211259 0.6966830 0.6757470 0.6450730
HR 0.8681501 0.7638721 0.6897677 0.5317619
RBI 0.8824090 0.8156612 0.7885666 0.6281239
AVG 0.7254274 0.7989005 0.7855945 0.5871543
OBP 0.7617499 0.8987390 0.7766375 0.7025979
SLG 1.0000000 0.9686752 0.8611140 0.6974086
OPS 0.9686752 1.0000000 0.8799893 0.7394981
WAR 0.8611140 0.8799893 1.0000000 0.8086359
Payroll.Salary2023 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: 0.000913#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: 0.000913#intercept is -2.74 shows a statistal significance #RBI, OBP, and OPS are not statistically significant predictors of Payroll Salary 2023 in this model as there p-values are greater than 0.05.
model6 = 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("C:/Users/duway/Downloads/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$Payroll.Salary2023))^2)
1 - SSE/SST[1] 0.5477734#plot the data and set the intercept to 0
plot(firstbase$RBI, firstbase$Payroll.Salary2023, xlab="RBI", ylab="Payroll Salary 2023", main="RBI vs Payroll Salary 2023")
abline(model1, col="red")