R Notebook

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** import the data **

# Load the data
baseball = read.csv("C:/Users/duway/Downloads/baseball.csv")
str(baseball)# check the structure of the data

getwd()# check the working directory

# create a subset of the data with only the columns we need
moneyball = subset(baseball,Year<2002)
str(moneyball)

902 rows and 15 columns

#Compute runs difference and add it to the dataframe as a new column RD
moneyball$RD = moneyball$RS - moneyball$RA
str(moneyball)

# plot rd and wins
plot(moneyball$RD, moneyball$W)

#Regression model to predict wins
WinsReg = lm(W ~ RD, data = moneyball)
summary(WinsReg)

for one unit increase in RD, the wins will increase by 0.1057661 or 10.57661%

# use the model to compute the predicted wins 100
Wins<-predict(WinsReg, data.frame(RD=100))
# w=81 + 0.1057661*100
Wins

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

a negative signal can signal a problem with multicollinearity

check correlation

cor(moneyball$BA, moneyball$OBP)

# run variance inflation factor from scratch
#install.packages("car")

#library(car)

# check for multicollinearity using the variance inflation factor
vif(RunsReg)

when you see greater than 5, it is a sign of multicollinearity

this shows a high correlation between BA and OBP

above these features show a high level of correlation with the runs scored

# use the model to compute the predicted runs
RunsReg = lm(RS ~ OBP + SLG , data = moneyball)
summary(RunsReg)

almost 92% of the variance in runs scored is explained by the model using OBP and SLG

Create a regression model to predict runs allowed

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

#oobp are the opponent’s on-base percentage and oslg is the opponent’s slugging percentage are both significant predictors of runs allowed #Is t-value is greater than 2, it is significant 9.979 for OOBP and 8.632 for OSLG

vif(RAReg)# check for multicollinearity

inclass activty seven

f a baseball team scores 763 runs and allows 614 runs, how many games do we expect the team to win?

Using the linear regression model constructed during the lecture, enter the number of games we expect the team to win:

# use the model to compute the predicted runs
Num_wins=88.88 + 0.1057661*(763-614)
Wins<-predict(WinsReg, data.frame(RD=763-614))
# w=81 + 0.1057661*100
Wins

The team is expected to win 97 games with 763 runs scored and 614 runs allowed difference of 149

inclass activty eight

Exercise 1 If a baseball team’s OBP is 0.361, SLG is 0.409, and BA is 0.257, how many runs do we expect the team to score? Using the linear regression model constructed during the lecture (the one that uses OBP, SLG, and BA as independent variables), find the number of runs we expect the team to score:

#If a baseball team’s OBP is 0.361, SLG is 0.409, and BA is 0.257, how many runs do we expect the team to score?
0

[1] 0

ExpectedRuns=-804.63 + 2737.77*(0.361) + 1584.91*(0.409)
ExpectedRuns # recheck the formula

[1] 831.9332

832 runs are expected to be scored by the team with OBP 0.361, SLG 0.409, and BA 0.257

Exercise 2

If a baseball team’s opponents OBP (OOBP) is 0.267 and opponents SLG (OSLG) is 0.392, how many runs do we expect the team to allow? Using the linear regression model discussed during the lecture (the one on the last slide of the previous video), find the number of runs we expect the team to allow.

#If a baseball team’s opponents OBP (OOBP) is 0.267 and opponents SLG (OSLG) is 0.392, how many runs do we expect the team to allow?

ExpectedRunsAllowed=-837.38 + 2913.60*(0.267) + 1514.29*(0.392)
ExpectedRunsAllowed

[1] 534.1529

534 runs are expected to be allowed by the team with OOBP 0.267 and OSLG 0.392