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I am examining the impact of 7 IVs on one DV using regression anaysis. Some of the IVs are significantly correlated with each other, which is consistent with theory.

While the single OLS regression between the individual IVs and the DV shows positive and significant effects in 4 out of 7 cases, multiple regression only finds 1 signigicant predictor.

As the first suspect in this case is multicollinearity, I applied a collinearity resistant Partial Least Squares Regression, which successfully identified 4 significant predictors.

However, when I conduct the VIF and Tolerance analysis, I don't find any indications for multicollinearity. VIF is below 1.7 for every variable.

  1. Do I have multicollinearity in the data?
  2. What else may explain this phenomenon?

(N = 80, survey data)

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    $\begingroup$ What you are asking is "how can adding six regressors to a (univariate) regression cause an originally "significant" result to be "insignificant"? What explanations are there beyond the obvious (there must be at least some collinearity)? This is extensively addressed in the duplicate. For a closely related thread, also see stats.stackexchange.com/questions/28474. $\endgroup$ – whuber Mar 11 '16 at 15:26