clear
set obs 50
generate z = rnormal() // this is the random effect
generate id = _n
expand 2
generate x = runiform()
generate y = 3 + 2*x + z + rnormal()
// Here, y=3+2*x is the fixed effect,
//   y = z is a random effect (a random intercept),
//   and y = rnormal() is the residual/error term.
//   In total we have y = fixed + random + residual.

xtset id
regress y x // incorrectly lumps variation due to id in with residual
est store under
xtreg y x // correct, random intercept model
mixed y x || id: // same model, mixed command
regress y x i.id // overfit
est store over
lrtest under over