###################################################################
# SpringMatrix Example -- Source code file spring-matrix-model1.r #
#                                                                 #
# Matrix calculations of regression model parameter estimates     #
# and standard errors for SpringReg Example using R               #
###################################################################

# Model 2: Simple Linear Regression.
cat(Model 2: Simple Linear Regression\n)

# Set up X matrix and y vector.
X = matrix(c(1, 0, 
	          1, 1, 
	          1, 2, 
	          1, 3, 
	          1, 4), 5, 2, byrow=T)
y = matrix(c(0,49,101,149,201), 5, 1, byrow=T)
cat("X matrix:\n")
print(X)
cat("y vector:\n")
print(y)

# Calculate estimated regression parameters.
beta = solve(t(X) %*% X) %*% t(X) %*% y
cat("beta vector:\n")
print(beta)

# Find the predicted value vector.
yhat = X %*% beta
cat("yhat vector:\n")
print(yhat)

# Find the residuals.
resids = y - yhat
cat("residual vector:\n")
print(resids)

# Compute SSE.
cat("Sum of squares for error (SSE):\n")
sse = t(resids) %*% resids
print(sse)

# Compute DFE
cat("Degrees of freedom for error (DFE):\n")
dfe = length(y) - 2
print(dfe)

# Compute MSE
cat("Mean of squares for error (MSE):\n")
mse = sse / dfe
print(mse)

# Calculate covariance matrix.
# Get MSE from SAS or R output.
covbeta = solve(t(X) %*% X) * as.numeric(mse)
cat("Covariance matrix for beta.\n")
print(covbeta)

# Calculate standard error of parameter estimate.
sdbeta = sqrt(diag(covbeta))
cat("Standard error of parameter estimate.\n")
print(sdbeta)


###############################################
# Output:                                     #
###############################################
Model 2: Simple Linear Regression
X matrix:
     [,1] [,2]
[1,]    1    0
[2,]    1    1
[3,]    1    2
[4,]    1    3
[5,]    1    4
y vector:
     [,1]
[1,]    0
[2,]   49
[3,]  101
[4,]  149
[5,]  201
beta vector:
     [,1]
[1,] -0.4
[2,] 50.2
yhat vector:
      [,1]
[1,]  -0.4
[2,]  49.8
[3,] 100.0
[4,] 150.2
[5,] 200.4
residual vector:
     [,1]
[1,]  0.4
[2,] -0.8
[3,]  1.0
[4,] -1.2
[5,]  0.6
Sum of squares for error (SSE):
[1] 3.6
Degrees of freedom for error (DFE):
[1] 3
Mean of squares for error (MSE):
[1] 1.2
Covariance matrix for beta.
      [,1]  [,2]
[1,]  0.72 -0.24
[2,] -0.24  0.12
Standard error of parameter estimate.
[1] 0.8485281 0.3464102