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How can a regression be significant yet all predictors be non-significant?

In a simple linear regression with multiple predictors, is it valid to interpret the significance of individual predictors even though the overall model is not significant?

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For another duplicate also see stats.stackexchange.com/questions/13850. – whuber♦ Sep 28 '12 at 22:56

marked as duplicate by whuber♦ Sep 28 '12 at 22:56

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I would be more comfortable answering this question if you provided more information. I think what you are saying is that the F statistic is not significant but given Y= a+B1+B2+B3+e you find a statistically significant t statistic on B1 and B3.

I'm then interpreting your question as whether you can make a valid statistical inference about B1 and B3 given a F statistic that is not significant.

The short answer is no.

In order to calculate a coefficient such as B1 you need to interpret the dependent variable Y at a statistically significant level which shows up in a significant F statistic.

See slide 7 here (http://monogan.myweb.uga.edu/teaching/ols/lm7.pdf) for the equation that calculates a coefficient. Notice the relationship with Y.

Does this help to answer your question?

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