Week 10
Author: Navdeep Metchu
Date: 2023-10-25
/* General Styles */
body {
font-family: 'Arial', sans-serif;
background-color: #f4f4f4;
margin: 0;
padding: 20px;
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header {
background-color: #333;
color: #fff;
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text-align: center;
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header h1 {
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header p {
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# Read the dataset
pokemon_data <- read.csv("PokemonStats.csv")Selecting an Interesting Binary Column
Binary Variable: “Is its total stat above 500?”
Yes (1)
No (0)
# Creating a new binary column 'HighTotalStat'
pokemon_data$HighTotalStat <- as.integer(pokemon_data$Total > 500)
# Displaying the first few rows of the dataset with the new column
head(pokemon_data[, c("Name", "Total", "HighTotalStat")])## Name Total HighTotalStat
## 1 Bulbasaur 318 0
## 2 Ivysaur 405 0
## 3 Venusaur 525 1
## 4 Venusaur Mega Venusaur 625 1
## 5 Charmander 309 0
## 6 Charmeleon 405 0We’ve created the binary variable HighTotalStat that indicates whether a Pokémon has a total stat above 500 (represented by 1) or not (represented by 0).
Building a Logistic Regression Model
For the logistic regression model, the dependent variable will be HighTotalStat, and we’ll choose 4 explanatory variables
To determine which explanatory variables might be most relevant for our logistic regression model, we’ll check the correlation of each potential variable with our target variable, HighTotalStat.
# Calculate correlation of potential explanatory variables with 'HighTotalStat'
correlations <- cor(pokemon_data[, c('HP', 'Attack', 'Defense', 'SpAtk', 'SpDef', 'Speed', 'Height', 'Weight', 'HighTotalStat')])['HighTotalStat',]
# Remove the correlation of 'HighTotalStat' with itself
correlations <- correlations[-which(names(correlations) == "HighTotalStat")]
# Sort correlations in descending order
sorted_correlations <- sort(correlations, decreasing=TRUE)
sorted_correlations## SpAtk Attack SpDef HP Defense Speed Height
## 0.5825124 0.5254463 0.5151532 0.4693824 0.4465165 0.4003035 0.2315656Based on the correlation values, the variables that have the highest correlation with our target variable HighTotalStat are:
SpAtk with a correlation of approximately 0.583
Attack with a correlation of approximately 0.525
SpDef with a correlation of approximately 0.515
HP (Hit Points) with a correlation of approximately 0.469
We’ll choose these 4
Building the logistic regression model using these variables.
X <- pokemon_data[, c('SpAtk', 'Attack', 'SpDef', 'HP')]
y <- pokemon_data$HighTotalStat
logit_model <- glm(y ~ SpAtk + Attack + SpDef + HP, data=pokemon_data, family=binomial(link="logit"))
summary(logit_model)##
## Call:
## glm(formula = y ~ SpAtk + Attack + SpDef + HP, family = binomial(link = "logit"),
## data = pokemon_data)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -21.587125 1.557261 -13.862 < 2e-16 ***
## SpAtk 0.063047 0.005516 11.430 < 2e-16 ***
## Attack 0.075208 0.006561 11.463 < 2e-16 ***
## SpDef 0.070693 0.007011 10.083 < 2e-16 ***
## HP 0.038298 0.005336 7.177 7.13e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1468.44 on 1193 degrees of freedom
## Residual deviance: 504.17 on 1189 degrees of freedom
## AIC: 514.17
##
## Number of Fisher Scoring iterations: 81. Coefficients:
The constant (or intercept) is −21.5871.
The coefficient for SpAtk is 0.0630.
The coefficient for Attack is 0.0752.
The coefficient for SpDef is 0.0707.
The coefficient for HP is 0.0383.
2. Interpretation:
Constant (−21.5871): This represents the log odds of a Pokémon having a total stat above 500 when all the explanatory variables are 0. Given that it’s not realistic for these stats to be zero, this value is mainly theoretical.
SpAtk: For a unit increase in the SpAtk value, the log odds of the Pokémon having a total stat greater than 500 increase by 0.0630, keeping all other variables constant.
Attack: For a unit increase in the Attack value, the log odds of the Pokémon having a total stat greater than 500 increase by 0.0752, keeping all other variables constant.
SpDef: For a unit increase in the SpDef value, the log odds of the Pokémon having a total stat greater than 500 increase by 0.0707, keeping all other variables constant.
HP: For a unit increase in the HP value, the log odds of the Pokémon having a total stat greater than 500 increase by 0.0383, keeping all other variables constant.
3. Significance:
All the explanatory variables have a p-value less than 0.05, which suggests that they are statistically significant predictors of whether a Pokémon has a total stat greater than 500.
pokemon_data$HighTotalStat <- as.integer(pokemon_data$Total > 500)
# List of explanatory variables
explanatory_vars <- c('SpAtk', 'Attack', 'SpDef', 'HP')
# Setting up the plotting parameters
par(mfrow=c(4,1), mar=c(4,4,2,1))
for (var in explanatory_vars) {
p <- ggplot(pokemon_data, aes(x=factor(HighTotalStat), y=get(var), fill=factor(HighTotalStat))) +
geom_boxplot() +
scale_fill_manual(values=c("#98A886", "#735290"), name="HighTotalStat", breaks=c(0, 1), labels=c("No", "Yes")) +
labs(title=paste('Box plot of', var, 'vs. HighTotalStat'),
x='HighTotalStat', y=var) +
theme_minimal() +
theme(
legend.position="top",
panel.background = element_rect(fill="lightgray", colour="black", linewidth=1),
panel.grid.major = element_line(colour = "white"),
panel.grid.minor = element_line(colour = "white", linetype = "dashed")
)
print(p)
}
