h3student.Rmd

---
title: "Assignment 3 ST464/ST684"
author: "Akshay Mishra(19250911)"
date: "`r format(Sys.time(), '%X %d %B, %Y')`"
output: html_document
editor_options: 
  chunk_output_type: inline
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, fig.width=4, fig.height=4)
```


```{r, eval=T, echo=FALSE}
suppressMessages(library(tidyverse))
suppressMessages(library(ggplot2))
suppressMessages(library(GGally))

```



#### Question 2



```{r eval=T} 
# change to eval=T
library(MASS)
library(ISLR)
library(class)
m <- median(Auto$mpg)
Auto$mpg01 <- factor(ifelse(Auto$mpg <= m, 0, 1))
 set.seed(1) 
s <- sample(nrow(Auto), round(.5*nrow(Auto)))
Atrain <- Auto[s,]
Atest <- Auto[-s,]
```

(a)
```{r}
ggplot(data=Atrain, aes(x=weight, y=acceleration, color=mpg01)) +
geom_point(alpha=.5)
```


(b)
```{r}
l <- lda(mpg01~weight+acceleration,data=Atrain)
l
plot(l)#plots of linear discriminants#additional content for explaination of lda if it is less than 0, then it falls in group0 otherwise in group1.
grid <- expand.grid(
weight = seq(1000, 5000, length = 100),
acceleration = seq(0, 35, length = 100)
)

grid$prob <- predict(l, grid)$posterior[,"1"]
ggplot(data=Atrain, aes(x=weight, y=acceleration)) +
geom_point(aes(color=mpg01),alpha=.5)+
geom_contour(data=grid,aes(z=prob),breaks=.5, color="black")

pred <- predict(l,newdata = Atest)$class
table(Atest$mpg01, pred)
mean(Atest$mpg01 != pred)
```

The test error of the model or the overall mis-classification rate is 12.7 %.

(c)
```{r}
q <- qda(mpg01~weight+acceleration,data=Atrain)
q
qda.grid <- expand.grid(
weight = seq(1000, 5000, length = 100),
acceleration = seq(0, 35, length = 100)
)

qda.grid$prob <- predict(q,qda.grid)$posterior[,"1"]
ggplot(data=Atrain, aes(x=weight, y=acceleration)) +
geom_point(aes(color=mpg01),alpha=.5)+
geom_contour(data=qda.grid,aes(z=prob),breaks=.5, color="black")


qpred <- predict(q,newdata = Atest)$class
table(Atest$mpg01, qpred)
mean(Atest$mpg01 != qpred)
```

The test error rate is 11.7 %. QDA is better than LDA as its test error rate is less than that of LDA.

(d)
```{r}
lda <- lda(mpg01~weight+acceleration+displacement+horsepower,data=Atrain)
lda

ldapred <- predict(lda,newdata = Atest)$class
table(Atest$mpg01, ldapred)
mean(Atest$mpg01 != ldapred)
```

The test error for this model obtained is 12.75 %.

(e)
```{r}
qda <- qda(mpg01~weight+acceleration+displacement+horsepower,data=Atrain)
qda

qdapred <- predict(qda,newdata = Atest)$class
table(Atest$mpg01, qdapred)
mean(Atest$mpg01 != qdapred)
```

Both LDA and QDA are better as their test error rates are same i.e. 12.75 %.

(f)
```{r}
xdatatrain <- scale(Atrain[,3:6])
means <- attr(xdatatrain,"scaled:center")
sds<- attr(xdatatrain,"scaled:scale")
xdataTest <- scale(Atest[,3:6], center=means, scale=sds)
p1 <- knn(xdatatrain, xdataTest, Atrain$mpg01, k=5)
t1 <- table(Atest$mpg01, p1)
t1
mean(Atest$mpg01 != p1)

p2 <- knn(xdatatrain, xdataTest, Atrain$mpg01, k=30)
t2 <- table(Atest$mpg01, p2)
t2
mean(Atest$mpg01 != p2)
```

The value of k=5 gives us a better result with test error rate of 11.7 % on the test set as its test error is less than that of k=30 which is 12.24 %.