# R code for least squares estimation of
# a simple linear regression model

# Consider the example on pg. 15 of the book

# response variable Y is "attempts"
# predictor variable X is "age"

age <- c(20, 55, 30)
attempts <- c(5, 12, 10)

# The above example is a reasonable way to enter 
# SMALL data sets into R.
# See Toluca data example on course web page for an 
# example of how to read in large data sets in R.

#######################################################

# fitting the regression model:

task.reg <- lm(attempts ~ age)

# Seeing the estimates (b_0 and b_1) of the regression coefficients:

task.reg

# Note the fitted regression equation is:
#
# Y-hat = 2.8077 + 0.1769X
#

# getting the summary regression output:

summary(task.reg)

# getting the ANOVA table:

anova(task.reg)

# Note MSE = 5.6538, and sqrt(MSE) = 2.378.
# (Can you find these in the R output?)

#########

# Plotting the data and the fitted regression line:

# Note that the plot function in R requires the X variable to be listed first
# (this is different than the plots in SAS):

plot(age, attempts)

# overlaying the regression line on this scatter plot:
abline(task.reg)