#read in the data from a csv file
dat1=read.table("Data Sets/Chapter 2/Examples/ex-2-1.csv", header=T, sep=",")

dat1 #print out the dat
y=dat1[,2] #assign the second column in dat1 to be variable y 
x=dat1[,3] #assign the third column in dat1 to be variable x 

#plot the data
plot(y~x)

fm1=lm(y~x)

summary(fm1)

anova(fm1)

resid(fm1)

df.residual(fm1)

coef(fm1)

#assign some notations
ybar=mean(y)
xbar=mean(x)
ei=resid(fm1)
yhat=fitted(fm1)
df=df.residual(fm1)

print(cbind(x,y,yhat, ei))

sum(ei^2)
sum(ei^2)/df
s2.hat=sum(ei^2)/df
sum((y-ybar)^2)
sum((yhat-ybar)^2)

#plot the data and the regression line 


plot(y~x)
lines(x, yhat, col=2)

Sxy=sum( (y-mean(y)) * (x-mean(x)) ); Sxy
Sxx=sum( (x-mean(x))^2 ); Sxx
sqrt(s2.hat * (1/20+mean(x)^2/Sxx))
sqrt(s2.hat/Sxx)


confint(fm1)

#install.packages("DAAG")
#library(DAAG)