data <- read.table("d:/PubH5470/LinearModelExample.txt", header=T)

#Reading the response

Y <- data$Y

#Length of Y

length(Y)

#Reading X

X <- as.matrix(data[,2:7])
#X <- cbind(data$X1,data$X2,data$X3,data$X4,data$X5,data$X6)

ones <- rep(1,times=length(Y))
#ones <- rep(1,times=nrow(X))

X <- cbind(ones,X)


#dimension of X

dim(X)

#Transpose of X is obtained by function t()

X.t <- t(X)

#Checking dimension of X.t

dim(X.t)

#Accessing Multivariate Normal in R

library(MASS)

help(mvrnorm)


#Detaching MASS

detach(package:MASS)





#Multiplication of matrices is done by %*% 

X.tX = X.t%*%X

#Inverse of a matrix is obtained by solve()

X.tX.inv <- solve(X.tX)

#Least squares estimate:

beta.hat <- X.tX.inv%*%X.t%*%Y


example.lm <- lm(Y ~ X[,1]+X[,2]+X[,3]+X[,4]+X[,5]+X[,6])

summary(example.lm)