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I have a small sample (30 obs) and 4 independent variables, 3 of which are significantly correlated to each other. I have tried to run the simple linear regression on each of them separately and it always turned out statistically significant but when I run the multiple linear regression with all of them together, each coefficient becomes highly non-significant (p-value>0.3) and also the overall model is non-significant.

I thought it must be a problem of multicollinearity, so I checked the variance inflation factor, which instead is small (always VIF<3) so I'm confused. Can I interpret at least the coefficients of the simple linear regressions or there is multicollinearity and I cannot isolate an independent variable from the others?

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  • $\begingroup$ Check out my answer here. It should answer all your questions except for the VIF question. $\endgroup$ – TrynnaDoStat Feb 19 '15 at 12:30

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