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Is it possible to interpret regression output when omitting the intercept? Can this omission be justified?

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  • $\begingroup$ The regression line will be $y=\frac{\mu_Y}{\mu_X}x$. It can have a positive slope even if correlation is negative (or the other way round). So to justify it, you need to believe that the ratio of the means carries all the useful information, and the rest is noise $\endgroup$ – Henry Feb 22 '14 at 19:54
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Heeding Nick's advice:

Some of the usual output in a regression can be interpreted. For example:

  • coefficients and standard errors are still meaningful

  • $s^2$ is still meaningful

  • the usual tests should still apply

The interpretations of these should proceed broadly as before, though the specific meaning of some coefficients will be different.

Some output has more difficulty of interpretation (for example, $R^2$ no longer means the same thing, and personally I avoid $R^2$ altogether in this case).

In some narrow situations, yes, it's justified to omit the intercept, but they're rare – and in each one of them I usually would fit it as well, or look at diagnostics specifically with the intent of identifying whether an intercept should be in the model.

As an example, in some physical situations, we 'know the model' has no intercept. (However, it's common in those cases for the other assumptions of regression to fail to hold, so something else than regression through the origin is often indicated anyway.)

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  • $\begingroup$ Now that I've got it, I can admit I was really just after the +2 rep for nitpicking your punctuation ;) $\endgroup$ – Nick Stauner Feb 20 '14 at 8:10
  • $\begingroup$ I approved it. There was enough there to make it worth fixing. You and Nick Cox should start a club - between you there's not much that gets through undetected. $\endgroup$ – Glen_b Feb 20 '14 at 8:13

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