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Two of my independent variables are correlated with the dependent variable but in multiple regression they turned out to be insignificant predictors of the same.

Is it possible? and how to report this difference in data interpretation?

Nick Cox
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bbw
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    Entirely possible and indeed very common. Significance of predictors will depend on what else is in the model. Should be discussed in any decent regression text or course. Similar issues discussed at http://stats.stackexchange.com/questions/14500/how-can-a-regression-be-significant-yet-all-predictors-be-non-significant – Nick Cox Feb 09 '14 at 11:03
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    It's even possible with only those two variables in the model. Consider a simple case, where $Y$ is correlated with $x_1$ and $x_2$. Very highly correlated. But now, on closer examination, $x_1$ and $x_2$ are almost perfectly correlated. Then each will be insignificant in the multiple regression. Examples are easily constructed. – Glen_b Feb 09 '14 at 11:22

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