getwd()
[1] "/cloud/project"
baseball = read.csv("baseball.csv")
str(baseball)
'data.frame':   1232 obs. of  15 variables:
 $ Team        : chr  "ARI" "ATL" "BAL" "BOS" ...
 $ League      : chr  "NL" "NL" "AL" "AL" ...
 $ Year        : int  2012 2012 2012 2012 2012 2012 2012 2012 2012 2012 ...
 $ RS          : int  734 700 712 734 613 748 669 667 758 726 ...
 $ RA          : int  688 600 705 806 759 676 588 845 890 670 ...
 $ W           : int  81 94 93 69 61 85 97 68 64 88 ...
 $ OBP         : num  0.328 0.32 0.311 0.315 0.302 0.318 0.315 0.324 0.33 0.335 ...
 $ SLG         : num  0.418 0.389 0.417 0.415 0.378 0.422 0.411 0.381 0.436 0.422 ...
 $ BA          : num  0.259 0.247 0.247 0.26 0.24 0.255 0.251 0.251 0.274 0.268 ...
 $ Playoffs    : int  0 1 1 0 0 0 1 0 0 1 ...
 $ RankSeason  : int  NA 4 5 NA NA NA 2 NA NA 6 ...
 $ RankPlayoffs: int  NA 5 4 NA NA NA 4 NA NA 2 ...
 $ G           : int  162 162 162 162 162 162 162 162 162 162 ...
 $ OOBP        : num  0.317 0.306 0.315 0.331 0.335 0.319 0.305 0.336 0.357 0.314 ...
 $ OSLG        : num  0.415 0.378 0.403 0.428 0.424 0.405 0.39 0.43 0.47 0.402 ...
#Here we are filter ing the data to only show data before 2002
moneyball = subset(baseball, Year < 2002)
str(moneyball)
'data.frame':   902 obs. of  15 variables:
 $ Team        : chr  "ANA" "ARI" "ATL" "BAL" ...
 $ League      : chr  "AL" "NL" "NL" "AL" ...
 $ Year        : int  2001 2001 2001 2001 2001 2001 2001 2001 2001 2001 ...
 $ RS          : int  691 818 729 687 772 777 798 735 897 923 ...
 $ RA          : int  730 677 643 829 745 701 795 850 821 906 ...
 $ W           : int  75 92 88 63 82 88 83 66 91 73 ...
 $ OBP         : num  0.327 0.341 0.324 0.319 0.334 0.336 0.334 0.324 0.35 0.354 ...
 $ SLG         : num  0.405 0.442 0.412 0.38 0.439 0.43 0.451 0.419 0.458 0.483 ...
 $ BA          : num  0.261 0.267 0.26 0.248 0.266 0.261 0.268 0.262 0.278 0.292 ...
 $ Playoffs    : int  0 1 1 0 0 0 0 0 1 0 ...
 $ RankSeason  : int  NA 5 7 NA NA NA NA NA 6 NA ...
 $ RankPlayoffs: int  NA 1 3 NA NA NA NA NA 4 NA ...
 $ G           : int  162 162 162 162 161 162 162 162 162 162 ...
 $ OOBP        : num  0.331 0.311 0.314 0.337 0.329 0.321 0.334 0.341 0.341 0.35 ...
 $ OSLG        : num  0.412 0.404 0.384 0.439 0.393 0.398 0.427 0.455 0.417 0.48 ...
#We are creating the Runs Difference column in the data set
moneyball$RD = moneyball$RS - moneyball$RA
str(moneyball)
'data.frame':   902 obs. of  16 variables:
 $ Team        : chr  "ANA" "ARI" "ATL" "BAL" ...
 $ League      : chr  "AL" "NL" "NL" "AL" ...
 $ Year        : int  2001 2001 2001 2001 2001 2001 2001 2001 2001 2001 ...
 $ RS          : int  691 818 729 687 772 777 798 735 897 923 ...
 $ RA          : int  730 677 643 829 745 701 795 850 821 906 ...
 $ W           : int  75 92 88 63 82 88 83 66 91 73 ...
 $ OBP         : num  0.327 0.341 0.324 0.319 0.334 0.336 0.334 0.324 0.35 0.354 ...
 $ SLG         : num  0.405 0.442 0.412 0.38 0.439 0.43 0.451 0.419 0.458 0.483 ...
 $ BA          : num  0.261 0.267 0.26 0.248 0.266 0.261 0.268 0.262 0.278 0.292 ...
 $ Playoffs    : int  0 1 1 0 0 0 0 0 1 0 ...
 $ RankSeason  : int  NA 5 7 NA NA NA NA NA 6 NA ...
 $ RankPlayoffs: int  NA 1 3 NA NA NA NA NA 4 NA ...
 $ G           : int  162 162 162 162 161 162 162 162 162 162 ...
 $ OOBP        : num  0.331 0.311 0.314 0.337 0.329 0.321 0.334 0.341 0.341 0.35 ...
 $ OSLG        : num  0.412 0.404 0.384 0.439 0.393 0.398 0.427 0.455 0.417 0.48 ...
 $ RD          : int  -39 141 86 -142 27 76 3 -115 76 17 ...
plot(moneyball$RD, moneyball$W)

#The RD absolutely effects the number of wins a team gets. 
# Regression model to predict wins
WinsReg = lm(W ~ RD, data=moneyball)
summary(WinsReg)

Call:
lm(formula = W ~ RD, data = moneyball)

Residuals:
     Min       1Q   Median       3Q      Max 
-14.2662  -2.6509   0.1234   2.9364  11.6570 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) 80.881375   0.131157  616.67   <2e-16 ***
RD           0.105766   0.001297   81.55   <2e-16 ***
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.939 on 900 degrees of freedom
Multiple R-squared:  0.8808,    Adjusted R-squared:  0.8807 
F-statistic:  6651 on 1 and 900 DF,  p-value: < 2.2e-16

RD does not effect the number of wins acccording to the estimate. 10 more RD it increases the number of wins by 1. The equation for Wins is W = 81 + 0.10 (RD).

In Class Activity 7

NumberofWins = 80.88 + 0.106*(763-614)
NumberofWins
[1] 96.674

A team with runs difference of 149 is expected to win around 97 games.

RunsReg = lm(RS ~ OBP + SLG + BA, data=moneyball)
summary(RunsReg)

**There is a problem with the model because BA and OBP are highly correlated and accordinf to the model the BA negatively impacte the OBP*

cor(moneyball$BA,moneyball$OBP)

This is a very high correlation which proves our point above that there is something wrong with the model

RunsReg = lm(RS ~ OBP + SLG, data=moneyball)
summary(RunsReg)

Call:
lm(formula = RS ~ OBP + SLG, data = moneyball)

Residuals:
    Min      1Q  Median      3Q     Max 
-70.838 -17.174  -1.108  16.770  90.036 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  -804.63      18.92  -42.53   <2e-16 ***
OBP          2737.77      90.68   30.19   <2e-16 ***
SLG          1584.91      42.16   37.60   <2e-16 ***
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 24.79 on 899 degrees of freedom
Multiple R-squared:  0.9296,    Adjusted R-squared:  0.9294 
F-statistic:  5934 on 2 and 899 DF,  p-value: < 2.2e-16

In Class Activity 8K Part A

ExpectedRuns = -804.63+2737.77*(0.361)+1584.91*(0.409)
ExpectedRuns
[1] 831.9332

We expect to score around 832 runs

Almost 93% of the data can be explained by the variables selected. 

RunsAllowedReg = lm(RA ~ OOBP + OSLG, data=moneyball)
summary(RunsAllowedReg)

Call:
lm(formula = RA ~ OOBP + OSLG, data = moneyball)

Residuals:
    Min      1Q  Median      3Q     Max 
-82.397 -15.178  -0.129  17.679  60.955 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  -837.38      60.26 -13.897  < 2e-16 ***
OOBP         2913.60     291.97   9.979 4.46e-16 ***
OSLG         1514.29     175.43   8.632 2.55e-13 ***
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 25.67 on 87 degrees of freedom
  (812 observations deleted due to missingness)
Multiple R-squared:  0.9073,    Adjusted R-squared:  0.9052 
F-statistic: 425.8 on 2 and 87 DF,  p-value: < 2.2e-16

OOBP and OSLG are both signifiant at a 5% significance level. They explain almost 90% of the varience in the model

In-Class Activity 8: Part B

ExpectedRunsAllowed = -837.38+2913.60*(0.267)+1514.29*(0.392)
ExpectedRunsAllowed
[1] 534.1529

We expect there to be about 534 runs allowed.

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