Activity6

##We are creating the dataframe with the csv file firebasestats
firstbase = read.csv("C:\\Users\\Frank\\Desktop\\Special Topics Sports  Analytics\\R\\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       
##  Length:23          Length:23          Length:23          Min.   :  5.0  
##  Class :character   Class :character   Class :character   1st Qu.:105.5  
##  Mode  :character   Mode  :character   Mode  :character   Median :131.0  
##                                                           Mean   :120.2  
##                                                           3rd Qu.:152.0  
##                                                           Max.   :160.0  
##        AB              H              X2B              HR       
##  Min.   : 14.0   Min.   :  3.0   Min.   : 1.00   Min.   : 0.00  
##  1st Qu.:309.0   1st Qu.: 74.5   1st Qu.:13.50   1st Qu.: 8.00  
##  Median :465.0   Median :115.0   Median :23.00   Median :18.00  
##  Mean   :426.9   Mean   :110.0   Mean   :22.39   Mean   :17.09  
##  3rd Qu.:558.0   3rd Qu.:146.5   3rd Qu.:28.00   3rd Qu.:24.50  
##  Max.   :638.0   Max.   :199.0   Max.   :47.00   Max.   :36.00  
##       RBI              AVG              OBP              SLG        
##  Min.   :  1.00   Min.   :0.2020   Min.   :0.2140   Min.   :0.2860  
##  1st Qu.: 27.00   1st Qu.:0.2180   1st Qu.:0.3030   1st Qu.:0.3505  
##  Median : 63.00   Median :0.2420   Median :0.3210   Median :0.4230  
##  Mean   : 59.43   Mean   :0.2499   Mean   :0.3242   Mean   :0.4106  
##  3rd Qu.: 84.50   3rd Qu.:0.2750   3rd Qu.:0.3395   3rd Qu.:0.4690  
##  Max.   :115.00   Max.   :0.3250   Max.   :0.4070   Max.   :0.5780  
##       OPS              WAR         Payroll.Salary2023
##  Min.   :0.5000   Min.   :-1.470   Min.   :  720000  
##  1st Qu.:0.6445   1st Qu.: 0.190   1st Qu.:  739200  
##  Median :0.7290   Median : 1.310   Median : 4050000  
##  Mean   :0.7346   Mean   : 1.788   Mean   : 6972743  
##  3rd Qu.:0.8175   3rd Qu.: 3.140   3rd Qu.: 8150000  
##  Max.   :0.9810   Max.   : 7.860   Max.   :27000000

Including Plots

# Linear Regression (one variable)
#We are creating our linear regression model, this being our first one
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 
##  13654950.2  10082148.6  -5524939.3  10298631.2   1626214.0  -6731642.8 
##           7           8           9          10          11          12 
##  -5902522.2 -10250330.7  -4711916.8   -532796.1  -6667082.5  -6696203.1 
##          13          14          15          16          17          18 
##   7582148.6  -4916640.9  -1898125.3   -336532.3   -995042.5  -1311618.3 
##          19          20          21          22          23 
##   -843454.5   8050721.3   1250336.9   1847040.4   2926656.0

#Second Linear Regression Model
# 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

# We are Removing HR from the formula this time
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: 0.00298

firstbase<-firstbase[,-(1:3)]

# Correlations betweens RBI and Payroll.salary2023
cor(firstbase$RBI, firstbase$Payroll.Salary2023)

## [1] 0.6281239

#correlation between OBP and AVG in firstbase dataframe
cor(firstbase$AVG, firstbase$OBP)

## [1] 0.8028894

#correlation matrix amongst all the variables
cor(firstbase)

##                           GP        AB         H       X2B        HR       RBI
## GP                 1.0000000 0.9779421 0.9056508 0.8446267 0.7432552 0.8813917
## AB                 0.9779421 1.0000000 0.9516701 0.8924632 0.7721339 0.9125839
## H                  0.9056508 0.9516701 1.0000000 0.9308318 0.7155225 0.9068893
## X2B                0.8446267 0.8924632 0.9308318 1.0000000 0.5889699 0.8485911
## HR                 0.7432552 0.7721339 0.7155225 0.5889699 1.0000000 0.8929048
## RBI                0.8813917 0.9125839 0.9068893 0.8485911 0.8929048 1.0000000
## AVG                0.4430808 0.5126292 0.7393167 0.6613085 0.3444242 0.5658479
## OBP                0.4841583 0.5026125 0.6560021 0.5466537 0.4603408 0.5704463
## SLG                0.6875270 0.7471949 0.8211406 0.7211259 0.8681501 0.8824090
## OPS                0.6504483 0.6980141 0.8069779 0.6966830 0.7638721 0.8156612
## WAR                0.5645243 0.6211558 0.7688712 0.6757470 0.6897677 0.7885666
## Payroll.Salary2023 0.4614889 0.5018820 0.6249911 0.6450730 0.5317619 0.6281239
##                          AVG       OBP       SLG       OPS       WAR
## GP                 0.4430808 0.4841583 0.6875270 0.6504483 0.5645243
## AB                 0.5126292 0.5026125 0.7471949 0.6980141 0.6211558
## H                  0.7393167 0.6560021 0.8211406 0.8069779 0.7688712
## X2B                0.6613085 0.5466537 0.7211259 0.6966830 0.6757470
## HR                 0.3444242 0.4603408 0.8681501 0.7638721 0.6897677
## RBI                0.5658479 0.5704463 0.8824090 0.8156612 0.7885666
## AVG                1.0000000 0.8028894 0.7254274 0.7989005 0.7855945
## OBP                0.8028894 1.0000000 0.7617499 0.8987390 0.7766375
## SLG                0.7254274 0.7617499 1.0000000 0.9686752 0.8611140
## OPS                0.7989005 0.8987390 0.9686752 1.0000000 0.8799893
## WAR                0.7855945 0.7766375 0.8611140 0.8799893 1.0000000
## Payroll.Salary2023 0.5871543 0.7025979 0.6974086 0.7394981 0.8086359
##                    Payroll.Salary2023
## GP                          0.4614889
## AB                          0.5018820
## H                           0.6249911
## X2B                         0.6450730
## HR                          0.5317619
## RBI                         0.6281239
## AVG                         0.5871543
## OBP                         0.7025979
## SLG                         0.6974086
## OPS                         0.7394981
## WAR                         0.8086359
## Payroll.Salary2023          1.0000000

#We are Removing the AVG from the formula
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

#making the linear model with only 1 instances of OBP
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

# Reading the new data file with _test at the end and turning it into a string
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
#making the prediction for the new test model 
predictTest = predict(model6, newdata=firstbaseTest)
predictTest

##        1        2 
## 10723186 11558647

# Computing R-squared formula for the prediction variables
SSE = sum((firstbaseTest$Payroll.Salary2023 - predictTest)^2)
SST = sum((firstbaseTest$Payroll.Salary2023 - mean(firstbase$Payroll.Salary2023))^2)
1 - SSE/SST

## [1] 0.5477734