Log-likelihood functions

These two ways of computing the log-likelihood (an automatic way and naive way) differ because sigma(m) estimates sigma so it applies a (1 / (N - p)) correction but logLik() does not.

m <- lm(mpg ~ wt + disp, mtcars)
logLik(m)
#> 'log Lik.' -78.08389 (df=4)

ls <- dnorm(mtcars$mpg, predict(m), sigma(m))
sum(log(ls))
#> [1] -78.15893