# R code for Lecture 2


# R code for chapter 1 (part 2)

# Example 1

mydata = read.table("data010201.txt")  #read the data 
X = mydata$V1   # select X
Y = mydata$V2   # select Y

plot(X, Y)  # plot the observations (data)

myreg = lm(Y~X) # do the linear regression 
summary(myreg)  # output the estimation

lines(X, myreg$fitted) # plot the fitted 

title("Scatter of (X,Y) and fitted linear regression model")

newX <- data.frame(X = c(-3, 3, 0.5))
predict(myreg, newX)


# Obtain confidence intervals for beta_0 and beta_1. 

confint(myreg, level=0.95)



# R code for chapter 1 (part 3)

mydata = read.table("data010301.txt")  
X = mydata$V1   # define X
Y = mydata$V2   # define Y

plot(X, Y)  # plot the observations (data)

myreg = lm(Y~X) # do the linear regression
summary(myreg)  # output the estimation

plot(X, Y)  # plot the observations (data)
lines(X, myreg$fitted) # plot the fitted

#part a
newX = data.frame(X = c(4))
predEY = predict(myreg, newX, interval="confidence", level=0.95)
predEY

#part b
newX = data.frame(X = c(4))
predY = predict(myreg, newX, interval="prediction", level=0.95)
predY

#part c
newX = data.frame(X = c(10:10:130))
predEYband = predict(myreg, newX, interval="confidence", level=0.95)

lines(data.matrix(newX), data.matrix(predEYband[,2]), col="red", lty=4)
                        # add red and dash lines for the upper band
lines(data.matrix(newX), data.matrix(predEYband[,3]), col="red", lty=4)
                        # add red and dash plot for the lower band


title('regression analysis for the Toluca Company data')