If the linear regression's f-test is insignificant but its coefficients are significant in t-test, can I use this regression and its coefficients?

In academic journals, I find people use linear regression without reporting f-test values but use its coefficients as long as they are significant.

Is it ok to use the linear regression's coefficients ignoring its f-test values?

  • 3
    $\begingroup$ The possible causes of such a situation are extensively discussed at stats.stackexchange.com/questions/24720. But if the F-test tells you the fit is insignificant, then you have no justification to look any further: doing so could validly be characterized as "p-hacking" or "data snooping." $\endgroup$ – whuber Jun 29 '17 at 14:52
  • $\begingroup$ So your short answer to the question is "No, you cannot use the coefficients although they are significant if the regression f-test is insignificant". $\endgroup$ – Eric Jun 29 '17 at 15:00
  • $\begingroup$ If you need a short answer: No. $\endgroup$ – Mark White Jun 29 '17 at 15:01
  • $\begingroup$ While this sequential testing procedure is used sometimes, there are situations where it seems quite rubbish. E.g. when confirming the result of a two-sample comparison by running a linear model with potential confounders. It all depends on the goal of your analysis. $\endgroup$ – Michael M Jun 29 '17 at 15:02
  • $\begingroup$ Then if the f-test is insignificant but coefficients are significant, I understand I cannot use these coefficients. But if I still need to report this regression, is it normal to show regression with insignificant f-test result but with significant coefficients although I do not interpret them at all? $\endgroup$ – Eric Jun 29 '17 at 15:15

F test is the first thing to do in regression after identifying the features and if it fails then it means that none of the predictors/features for the given degrees of freedom is significant, so stop there. Now, I get this question a lot that if we have any single significant predictor present in the model then why bother an $F$ test. The answer here is that suppose we have $100$ predictors and we do not do an $F$ test and just rely on $t$ test to see if any predictor is significant using p-value $\le 0.05$ and then proceed with those which are significant, then there is a serious problem with this approach which is, that by chance we will have $5$ out of $100$ predictors which won't be significant but will have low p value due to chance alone. This is the reason an $F$ test is important and the first criteria to fit a model.

| cite | improve this answer | |

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.