0
$\begingroup$

Is there a way to analytically determine the new coefficients without re-estimating the regression? To give you a concrete example that might make answering easier, consider the following two models. Let's say I have b1 and b2, and would like to know what b3 and b4 would be?

(Model 1) y = b1 + b2*x

(Model 2) log(y) = b3 + b4*x

$\endgroup$

1 Answer 1

1
$\begingroup$

With simple linear regression, you can save a little calculation -- essentially those quantities from the first regression that don't depend on $y$ can be reused (so $n$ and the mean and variance of $x$, or equivalent information). Except in some very paricular situations, the mean of the transformed $y$, the variance of the transformed $y$ and the covariance of $x$ with the transformed $y$ (or equivalent information) will have to be obtained from the data.

However, with larger models (multiple regression) and large sample sizes it can save a fair bit of time to save the corresponding information from the first regression (in particular, you could save the QR decomposition of the $X$-matrix, avoiding the need to recalculate it). If numerical stability is not going to be an issue you can sometimes go a bit further. In extremely stable cases with few predictors and large sample size and many different response vectors to calculate the regression on, you might even consider progressing to $(X^\top X)^{-1}$, but this is usually not a suitable strategy.

$\endgroup$
2
  • $\begingroup$ +1 for constructive ideas. Wouldn't it be better, though, to signal a plain answer by starting this post with a great big "NO"? $\endgroup$
    – whuber
    Commented Jun 8, 2018 at 12:44
  • 1
    $\begingroup$ The gist of my answer is nearer to "sort of" than "no" -- you don't need to re-do everything from scratch, because you can reuse a substantive fraction of the calculations involving only the predictors (but of course no matter what you do you re-estimate a regression, since that's entirely the point; any shortcut to the coefficients is still in some sense re-estimation, so it's always both 'ýes' and 'no). $\endgroup$
    – Glen_b
    Commented Jun 8, 2018 at 14:00

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

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