All the interesting regression quantities

regression.R

# Randomly generate some data
S <- rWishart(1, 10, diag(10))[,,1] / 10
X <- MASS::mvrnorm(100, rep(0, 10), S)
b <- runif(10, -1, 1)
y <- X %*% b + rnorm(100, sd = sqrt(b %*% S %*% b))


# all the interesting regression quantities!
n    <- nrow(X)                       # sample size
p    <- ncol(X)                       # parameters in model matrix
xtxi <- solve(crossprod(X))           # inverse covariance matrix
xty  <- crossprod(X, y)               # covariance of X with y
bhat <- xtxi %*% xty                  # beta estimates
yres <- y - X %*% bhat                # residuals
rss  <- crossprod(yres)               # residual sum of squares
rdf  <- n - p                         # degrees of freedom
acov <- as.numeric(rss / rdf) * xtxi  # asymptotic covmat of beta
bse  <- sqrt(diag(acov))              # standard error of beta
tb   <- bhat/bse                      # t scores of beta
pval <- 2 * (1 - pt(tb, df = rdf))    # p values of beta