week-10

library(ggthemes)
library(ggrepel)

## Loading required package: ggplot2

library(AmesHousing)
library(boot)
library(broom)
library(lindia)
Data_set <- "/Users/ba/Documents/IUPUI/Masters/First Sem/Statistics/Dataset/PitchingPost.csv"
Pitching_Data <- read.csv(Data_set)

• We will be creating a binary variable from the round column. The pitchers who played in the world series will denoted with “1”, and who didn’t get to play in the world series will be denoted with “0”. And we aim to classify this based on the metric “IPouts”

Pitching_Data$played_in_WS <- ifelse(Pitching_Data$round == "WS", 1, 0)

Pitching_Data |>
  ggplot(aes(x=IPouts,y=played_in_WS))+
  geom_jitter(width = 0, height = 0.1, shape = 'O', size = 3) +
  geom_point()+
  geom_smooth(method = "lm",se=FALSE)+
  theme_economist()

## `geom_smooth()` using formula = 'y ~ x'

• Logistic Regression

model <- glm(played_in_WS ~ IPouts, family = binomial, data = Pitching_Data)
model

## 
## Call:  glm(formula = played_in_WS ~ IPouts, family = binomial, data = Pitching_Data)
## 
## Coefficients:
## (Intercept)       IPouts  
##    -2.22412      0.02834  
## 
## Degrees of Freedom: 3749 Total (i.e. Null);  3748 Residual
## Null Deviance:       2953 
## Residual Deviance: 2915  AIC: 2919

Interpretation:

• Intercept (-2.22412): This value represents the log-odds of a player having played in the World Series when the number of innings pitched outs (IPouts) is zero. In practical terms, it suggests that a player with no innings pitched outs is quite unlikely to have played in the World Series, given the negative coefficient.

• IPouts (0.02834): This coefficient tells us how the log-odds of having played in the World Series changes with each additional inning pitched out. The positive sign indicates that as the number of innings pitched outs increases, so does the likelihood of having played in the World Series. Each additional out increases the log-odds of having played in the World Series by 0.02834.

Since logistic regression models the log-odds, the interpretation in terms of probability is non-linear:

• For small increases in IPouts, the probability of having played in the World Series increases, but the relationship is not straightforward because it’s on a log-odds scale.

• To interpret the change in probability, one could calculate the odds ratio, which is exp(0.02834) ~ 1.0287. This means that each additional out pitched increases the odds of having played in the World Series by approximately 2.87%.

• Confidence Interval

ci <- confint(model, "IPouts", level = 0.95)

## Waiting for profiling to be done...

ci

##      2.5 %     97.5 % 
## 0.01949196 0.03703962

Interpretation:

This confidence interval indicates that we are 95% confident that the true coefficient for IPouts lies between approximately 0.01949 and 0.03704. The interval does not include zero, which strongly suggests that the relationship between IPouts (Innings Pitched Outs) and the likelihood of a player having played in the World Series is statistically significant. This reaffirms the finding that more innings pitched (more outs) are associated with a higher likelihood of playing in the World Series.

The coefficient indicates the change in the log-odds of having played in the World Series for each additional out pitched. Specifically, the interval suggests that for each additional out pitched, the log-odds of playing in the World Series increases by between approximately 0.0195 and 0.0370.