#-0 Preliminaries

    inv = solve #Define inv() as inverse for a matrix
    
    W = matrix(c(1,2,3,4),ncol=2)
    V = matrix(c(5,6,7,8,9,10),ncol=2)
    W
    inv(W)
    V    
    t(V)    # transpose of matrix W
    V %*% W # matrix multiplication of V & W
    W %*% V   
    W %*% inv(W) # 2x2 identity matrix
    
#-1 Create data in terms of matrix X and vector Y
    Y  = c(5,7,8,9)
    X1 = c(1,2,2,3)
    n  = length(Y)

#-2 Fit a linear model
    mod = lm(Y ~ X1)
    mod
    attributes(mod) #objects available via mod$

#-3 Create the "design matrix" X
    X0 = c(1,1,1,1)
    X  = cbind(X0,X1) # column bind 2 vectors together
    X
    
#-4 Create the X'X matrix and its inverse

#** FOR 5-13 IDENTIFY WHAT PORTIONS OF THE R OUTPUT FROM BUILT-IN FUNCTIONS
#** CORRESPOND TO (OR DIFFER FROM) THE MATRIX COMPUTATION.
        
#-5 Compute Beta.hat by matrix multiplication
#   Compare to mod$coeff

#-6 Compute Y.hat by matrix multiplication
#   Compare to mod$fitted and predict(mod)

#-7 Compute the residuals using matrix (vector) arithmetic (i.e., subtraction)
#   Compare to mod$resid

#-8 Compute the SSE & MSE from (7) using using matrix (vector) arithmetic
#   Compute this again using the sum() function
#   Compare to anova(mod)

#-9 Compute the correlation between Y and X1    and square it
#   Compute the correlation between Y and Y.hat and square it
#   Compare to values from summary(mod)
   
#10 Compute the leverage values by matrix multiplication 
#   Compare to hatvalues(mod) 

#11 Compute the (internally) standardized residuals using vector arithmetic 
    Compare to rstandard(mod)

#12 For #4, compute the X'X matrix and its inverse by hand

#13 Use the 3rd standardized residual, r[3], and 3rd hatvalue, h[3], to compute 
#   the 3rd Cook's Distance
#   Compare to cooks.distance(mod)