# This sample program illustrate simple linear regression and
# polynomial regression of second order. 

# Refer to 
# http://lib.stat.cmu.edu/DASL/Stories/tvads.html
# for background of the data

# 1. Initiate an R section
# 2. Change the working dir to the one where the data is located.

# Reading data and assigned it as the working data set
tvad <- read.table("tvad.txt", header=T)
attach(tvad)

# Prelim inspection
tvad
# Initiate graphic devices 
par(mfrow=c(2,2));

hist(spend); boxplot(spend); qqnorm(spend);
plot(density(spend));

stem(spend) ; summary(spend);

hist(yields); boxplot(yields); qqnorm(yields);
plot(density(yields));

stem(yields) ; summary(yields);

plot(yields~spend)

fm0 <- lm(yields~1)                  # Summarization by mean only.
summary(fm0)		# Yields = b_0 + epsilon
# Plot the fitted line overlayed over the y vs. x scatter plot
plot(spend,yields,xlab="spend", ylab="yields", main="Summary by mean");
abline(coef(fm0),0)
# Plots for diagnosis
par(mfrow=c(2,2));
plot(fm0)

fm1 <- lm(yields~spend) # Regress yields on spend.
summary(fm1)		# Yields = b_0 + b_1 (spend) + epsilon
names(fm1)		# List variables from the regression output
# Plot the fitted line overlayed over the y vs. x scatter plot
plot(spend,yields,xlab="spend", ylab="yields", main="Simple Linear Regression");
abline(coef(fm1))
# Plots for diagnosis
par(mfrow=c(2,2));
plot(fm1)


fm2 <- lm(yields~spend+I(spend^2))
summary(fm2)
par(mfrow=c(2,2));
plot(fm2)
plot(spend,yields,xlab="spend", ylab="yields", main="Polynomial Regression");
hat<-predict(fm2)
points(approx(spend, hat), col = 2, pch = "*")

detach(tvad)
q()
# Exit (You don't need to save workspace image)