Question

what is the difference between stochastic disturbance term and the residual

Answer 1

$\Small \blue {\sf {Bonjour Mate!}}$

There is a theoretical model underlying any regression analysis. Consider

yi=βXi+uiyi=βXi+ui

where yiyi is the explained variable, XiXi are the independent variables and uiui is a random error. This random error (or stochastic disturbance) is not observed. We now estimate ββ as β^β^. Substituting this estimate into the equation we get

yi=β^Xi+ϵiyi=β^Xi+ϵi

where ϵiϵi is the residual in the estimated equation. \epsiloniepsiloni is not, in general, equal to uiui. as β^β^ is not equal to ββ. The residual is observed. The error is not observed.