### HW 7 solutions
### AHW3
### December 3, 2007

rm(list = ls())
############################################
## 1
y <- matrix(c(15,9,3,25,7,13), 6,1)
z <- cbind(rep(1,6), c(10, 5, 7, 19, 11, 8))
n <- nrow(y)
p <- ncol(y)

## calculate beta.hat
beta.hat <- solve(t(z)%*%z)%*%t(z)%*%y
beta.hat

## calculate y.hat (the fitted values)
y.hat <- z%*%beta.hat
y.hat

## calculate epsilon.hat (the residuals)
eps.hat <- y-y.hat
eps.hat

## calculate the cross products of the residuals
eps.hat.eps.hat <- t(eps.hat)%*%eps.hat
eps.hat.eps.hat

############################################
## 2
rm(list = ls())

y <- matrix(c(5,-3,3,-1,4,-1,2,2,1,3), 5,2, byrow=T)
z <- cbind(rep(1,5), c(-2,-1,0,1,2))
n <- nrow(y)
p <- ncol(y)

## calculate beta.hat
beta.hat <- solve(t(z)%*%z)%*%t(z)%*%y
beta.hat

## calculate y.hat (the fitted values)
y.hat <- z%*%beta.hat
y.hat

## calculate epsilon.hat (the residuals)
eps.hat <- y-y.hat
eps.hat

## calculate the cross products of the residuals
eps.hat.eps.hat <- t(eps.hat)%*%eps.hat
eps.hat.eps.hat