I have a regression, say $Y=a+bX_1+cX_2+e$.

I know how to do the standard $F$-test for $b=c=0$. However, in my case, both coefficients $b$ and $c$ should be positive. So is there a way to test if $b>0$ AND $c>0$? This would be a one-tailed $F$-test with two restrictions.

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    $\begingroup$ The first thing you mention is a null; presumably you mean against an alternative of at least one not being 0. Is the second thing mean to be an alternative hypothesis rather than a null? $\endgroup$ – Glen_b Nov 3 '15 at 9:14
  • $\begingroup$ I want to test the null $b>0$ AND $c>0 $ $\endgroup$ – user93929 Nov 3 '15 at 12:19
  • $\begingroup$ A composite null that doesn't include its boundary? I don't think that's going to work even for one variable. $\endgroup$ – Glen_b Nov 3 '15 at 12:28
  • $\begingroup$ Interesting question. I encountered multiple one-sided restrictions before in an econometrics class, and if I remember correctly it was generally impossible to test for. $\endgroup$ – Richard Hardy Nov 3 '15 at 16:03
  • $\begingroup$ Related: One-tailed F-test with one restriction. $\endgroup$ – Richard Hardy Mar 11 '17 at 15:47

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