## Calculate semi-partial and partial R2 values in a bivariate
## regression setting while systematically varying the correlation
## between the two covariates.


## Sample size.
n = 100

M = NULL

for (r in seq(-0.9, 0.9, 0.1)) {

  sp_r2 = NULL
  p_r2 = NULL

  ## Do replications to get a more stable result.
  for (k in 1:100) {
    
    ## Generate the design matrix.
    X1 = rnorm(n)
    U = rnorm(n)
    X2 = r*X1 + sqrt(1-r^2)*U
    X = cbind(X1, X2)
    
    ## Simulate the response.
    Y = X1 + X2 + rnorm(n)
    
    ## Calculate the full model R^2.
    m_full = lm(Y ~ X)
    R2_full = cor(Y, m_full$fitted.values)^2
    
    ## Calculate the submodel R^2 for X2 only.
    m_2 = lm(Y ~ X2)
    R2_2 = cor(Y, m_2$fitted.values)^2
    
    ## The semi-partial and partial R^2.
    sp_r2[k] = R2_full- R2_2
    p_r2[k] = sp_r2[k]/(1-R2_2)
  }
    
  M = rbind(M, c(r, mean(sp_r2), mean(p_r2)))
}