(Ugarte, Probability and Statistics with R, 2E) In the book, it reads:
$SST$: Sum of squares of Total.
$SSE$: Sum of squares of Error.
$SSR$: Sum of squares of Regression.

Marginal increases when adding x2 to a model that already contains x1 will be denoted as

$SSR(x2|x1) = SSR(x2,x1) - SSR(x1)$

which is equivalent to

$SSR(x2|x1) = SSE(x1) - SSE(x1,x2)$.

Why is there an equivalence?

What I did:

$SSR(x2|x1) = SSR(x2,x1) - SSR(x1)$ (using $SST=SSR+SSE$)

$= SST(x2,x1) - SSE(x2,x1) - [SST(x1) - SSE(x1)] $

$= SSE(x1) - SSE(x2,x1) + [SST(x2,x1) - SST(x1)]$.

So, in fact, the question turns out to be why $SST(x2,x1) - SST(x1) = 0$!



$$SST(X) = \sum_{i=1}^N(y_i - \bar{y})^2$$

so it doesn't depend on $X$.

  • $\begingroup$ So, it seems the exact value of that sum is irrelevant since the cancellation happens in $SST(x2,x1)−SST(x1)$ ? $\endgroup$ Mar 6 '17 at 15:56
  • $\begingroup$ @ErdoganCEVHER Exactly $\endgroup$ Mar 6 '17 at 16:22

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.