Matrix Algebra for Regression

reg matrice.r

# to support: http://econometricsense.blogspot.com/2011/11/basic-econometrics-in-r-and-sas.html
#------------------------------------------------------------
#  regression with canned lm routine
#------------------------------------------------------------
 
# read in data manually
 
x <- c(1,2,3,4,5) # read in x -values
 
y <- c(3,7,5,11,14) # read in y-values
 
data1 <- data.frame(x,y) # create data set combining x and y values
 
# analysis
 
plot(data1$x, data1$y) # plot data 
reg1 <- lm(data1$y~data1$x) # compute regression estimates
summary(reg1)              # print regression output
abline(reg1)               # plot fitted regression line

#------------------------------------------------------------
#   matrix programming based approach
#------------------------------------------------------------
 
# regression matrices require a column of 1's in order to calculate 
# the intercept or constant, create this column of 1's as x0
 
x0 <- c(1,1,1,1,1) # column of 1's
x1 <- c(1,2,3,4,5) # original x-values
 
# create the x- matrix of explanatory variables
 
x <- as.matrix(cbind(x0,x1))
 
# create the y-matrix of dependent variables
 
y <- as.matrix(c(3,7,5,11,14))
 
# estimate  b = (X'X)^-1 X'y
 
b <- solve(t(x)%*%x)%*%t(x)%*%y
 
print(b) # this gives the intercept and slope - matching exactly 
         # the results above