---
layout: post
title: "ISL: Chaper 3"
published: yes
---

## Bài 8

```{r label="mpg vs horsepower"}
# fileUrl <- "http://www-bcf.usc.edu/~gareth/ISL/Auto.csv"
# download.file(fileUrl,destfile="./ISL/Auto.csv")
auto=read.csv("./ISL/Auto.csv")
auto=na.omit(auto)
names(auto)
auto$horsepower=as.numeric(auto$horsepower)
lmout=lm(mpg ~ horsepower,data=auto)
summary(lmout)
predict(lmout,data.frame(horsepower=98))
predict(lmout,data.frame(horsepower=98),interval="confidence")
predict(lmout,data.frame(horsepower=98),interval="prediction")
plot(auto$horsepower,auto$mpg,col=3)
abline(lmout,lwd=3,col=2)
plot(predict(lmout), residuals(lmout))
plot(predict(lmout), rstudent(lmout))
par(mfrow=c(2,2))
plot(lmout)
```

## Bài 9

```{r label="mul"}
pairs(auto)
str(auto)
pairs(auto[c(1:6)])
cor(auto[c(1:6)])
lmout2=lm(mpg~.-name,data=auto)
summary(lmout2)
par(mfrow=c(2,2))
plot(lmout2)
```

## Bài 10

```{r label="carseats"}
library(ISLR)
names(Carseats)
attach(Carseats)
lmsales=lm(Sales~Price+Urban+US)
summary(lmsales)
contrasts(Urban)
summary(lm(Sales~Urban))
lmsales2=lm(Sales~Price+US)
summary(lmsales2)
coef(summary(lmsales2))
```

## Bài 11

```{r}
set.seed(1)
x=rnorm(100)
y=2*x+rnorm(100)
lmyx=lm(y~x-1)
# or lmxy=lm(y~x+0)
summary(lmyx)
lmxy=lm(x~y-1)
summary(lmxy)
summary(lm(x~y))
summary(lm(y~x))
```

## Bài 13

```{r label="noise"}
set.seed(28)
x=rnorm(100)
eps=rnorm(100,sd=0.25)
y=-1+0.5*x+eps
lm13=lm(y~x)
summary(lm13)
plot(x,y)
abline(lm13,col=2,lwd=2)
abline(-1,0.5,col=3,lwd=2)
legend(-2.5,0.3,c("Least square lines","Population regression line"),col=c(2,3),lwd=2)

lmx2=lm(y~x+I(x^2))
anova(lmx2,lm13)
```

## Bài 14

```{r label="collinearity"}
set.seed(1)
x1=runif(100)
x2=0.5*x1+rnorm(100)/10
y=2+2*x1+0.3*x2+rnorm(100)
cor(x1,x2)
pairs(data.frame(x1,x2,y),col=2)
summary(lm(y~x1+x2))
summary(lm(y~x1))
summary(lm(y~x2))

x1=c(x1,0.1)
x2=c(x2,0.8)
y=c(y,6)
summary(lm(y~x1+x2))
summary(lm(y~x1))
summary(lm(y~x2))
par(mfrow=c(2,2))
plot(lm(y~x1+x2))
plot(lm(y~x1))
plot(lm(y~x2))
```