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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?


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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