text: why is it always true tht d sse of a restricted model is at least as large as tht of tht d unrestricted model? i know that this is an intuition with the equation of sst=ssr+sse, but why is it true? for the same reason that the highest mountain in the world is at least as high as the highest mountain in us.  unrestricted model includes the restricted one as a special case, i.e. as a subset of coefficients that go into it. most estimation choose coefficients that minimize the error. wider set of coefficients to choose from means that errors cannot increase.   proof: if you have an estimate from restricted model, the coefficients are still valid for unrestricted model & generate same error. if some unrestricted coefficients give you lower error, good; if not - you still have restricted estimate and it's error.