###################################################################
# 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 1: Regression through the origin.
cat("Model 1: Regression Though the Origin\n")

# Set up X matrix and y vector.
X = matrix(0:4, 5, 1, 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) - 1
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 1: Regression Though the Origin
X matrix:
     [,1]
[1,]    0
[2,]    1
[3,]    2
[4,]    3
[5,]    4
y vector:
     [,1]
[1,]    0
[2,]   49
[3,]  101
[4,]  149
[5,]  201
beta vector:
         [,1]
[1,] 50.06667
yhat vector:
          [,1]
[1,]   0.00000
[2,]  50.06667
[3,] 100.13333
[4,] 150.20000
[5,] 200.26667
residual vector:
           [,1]
[1,]  0.0000000
[2,] -1.0666667
[3,]  0.8666667
[4,] -1.2000000
[5,]  0.7333333
Sum of squares for error (SSE):
Degrees of freedom for error (DFE):
Mean of squares for error (MSE):
Covariance matrix for beta.
           [,1]
[1,] 0.03222222
Standard error of parameter estimate.
[1] 0.1795055
> source(spring.r)
Model 1: Regression Though the Origin
X matrix:
     [,1]
[1,]    0
[2,]    1
[3,]    2
[4,]    3
[5,]    4
y vector:
     [,1]
[1,]    0
[2,]   49
[3,]  101
[4,]  149
[5,]  201
beta vector:
         [,1]
[1,] 50.06667
yhat vector:
          [,1]
[1,]   0.00000
[2,]  50.06667
[3,] 100.13333
[4,] 150.20000
[5,] 200.26667
residual vector:
           [,1]
[1,]  0.0000000
[2,] -1.0666667
[3,]  0.8666667
[4,] -1.2000000
[5,]  0.7333333
Sum of squares for error (SSE):
[1] 3.866667
Degrees of freedom for error (DFE):
[1] 4
Mean of squares for error (MSE):
[1] 0.9666667
Covariance matrix for beta.
           [,1]
[1,] 0.03222222
Standard error of parameter estimate.
[1] 0.1795055