# CrudeOil Example -- source code file crude-oil.R
# Find the estimated regression parameters using
# proc reg and also using the matrix regression model.  
# Also find the residuals and predicted values.

x1 <- c(1000, 1000, 1000, 2000, 2000, 
        2000, 3000, 3000, 3000)
x2 <- c(0, 15, 30, 0, 15, 30, 0, 15, 30)
y <- c(60.58, 72.72, 79.99, 66.83, 80.78,
       89.78, 69.68, 80.31, 91.99)

model <- lm(y ~ x1 + x2)

cat("MultiReg regression output\n")
print(summary(model))

cat("\n\nEstimated regression parameters\n")
cat("using beta = (X'X)^-1 X'Y.\n")

X <- cbind(rep(1, length(x1)), x1, x2)
cat("\nMatrix X:\n")
print(X)

Y <- matrix(y, length(y), 1)
cat("Matrix Y:\n")
print(Y)

beta <- solve(t(X) %*% X) %*% (t(X) %*% Y)
cat("\nEstimated Parameter Vector beta:\n")
print(beta)