Question: Consider the linear regression models FullModel: Y =X+e; Null Model : Y = e, where X Rnp is of full column rank. Assume that condition

  1. Consider the linear regression models
  2. FullModel: Y =X+e;
  3. Null Model : Y = e,
  4. where X Rnp is of full column rank. Assume that condition (N) holds. Let
  5. A Rpp be the identity matrix. Prove that
  6. (RSSnull RSSfull)/(dfnull dffull) = (A){A(XX)1A}1A/p,
  7. RSSfull /df full 2
  8. where and are least squares estimators derived from the full model.

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