#Intro Stuff
library(MASS) 
library(gmodels)
library(dplyr) 
library(ggplot2) 


#T-test/ANOVA Example:
head(cabbages)

#normality
hist(cabbages$HeadWt, col="green")
qqnorm(cabbages$HeadWt, col="green", pch=16)
qqline(cabbages$HeadWt)

#homogeneity of variance
boxplot(cabbages$HeadWt ~ cabbages$Cult, 
        ylab="Head Weight", 
        xlab="Cultivar", col="green")

var_c39 <- var(cabbages$HeadWt[cabbages$Cult=='c39'])
var_c52 <- var(cabbages$HeadWt[cabbages$Cult=='c52'])

var_c39
var_c52

var_c52/var_c39


#Regression Example
head(airquality)
airquality2 <-na.omit(airquality)

#linearity and homoscedacitiy
plot(airquality2$Solar.R, airquality2$Ozone)
plot(airquality2$Wind, airquality2$Ozone)
plot(airquality2$Temp, airquality2$Ozone)

lm1 <-lm(Ozone~Solar.R + Wind + Temp, data=airquality2)
plot(lm1)

#multicollinearity
airqualityX <- (airquality2[,2:4])
cor(airqualityX)


#Chi-square example
Titanic2 <- Titanic[,,2,2] #adults who survived by class and sex

Expected_M <-sum(Titanic2[1:4,1])/length(Titanic2[1:4,1]) 
Expected_F <-sum(Titanic2[1:4,2])/length(Titanic2[1:4,2]) 

Expected_M #84.5
Expected_F #79