library(tidyverse)
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library(ggplot2)
library(dbplyr)
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##     ident, sql
library(ggthemes)
library(ggrepel)
library(ggrepel)
library(broom)
library(lindia)
week3_dataset <- read.csv("baseball.csv",header = TRUE)

The Binary Data I choose is whether a team made the playoffs or not

week3_dataset <- week3_dataset %>%
  mutate(win_square = sqrt(W))

sigmoid <- \(x) 1 / (1 + exp(-(-5 + 0.15 * x)))

week3_dataset %>%
  ggplot(mapping = aes(x = W, y = Playoffs)) +
  geom_jitter(width = 0, height = 0.1, shape = 'O', size = 3) +
  geom_function(fun = sigmoid, color = 'blue', linewidth = 1)+
  labs(title = "Modeling a Binary Response with Playsoff teams and Wins") +
  scale_y_continuous(breaks = c(0, 1)) +
  theme_minimal()

model <- glm(Playoffs ~ W, data = week3_dataset,
             family = binomial(link = 'logit'))
model$coefficients
## (Intercept)           W 
##  -34.206104    0.372348
a <- exp(1)
b <- a ^ 0.372348
b
## [1] 1.451138

Each win will increase 45% chance of going to the postseason

model <- lm(Playoffs ~ W,
            data = week3_dataset)

plots <- gg_diagnose(model, plot.all = FALSE)
plot_all(plots[c('res_fitted', 'qqplot')], max.per.page = 1)

#I don't need transformation, since the residuals is very consistent.