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I did learn about collinearity issue where it is possible that 2 significant independent variables when used together in the model can make either or both insignificant. However does the vice-versa case exist? and under which circumstances?

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  • $\begingroup$ +1 first, i think the answer is yes, but i am struggling to give you a numerical example. $\endgroup$ – Haitao Du Aug 22 '16 at 4:56
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In general and dismissing collinearity , linear models become more representative as variables are introduced even though R^2 is relatively low in business application. Literature exists explaining this rational. During data exploratory practice one may find two less significant variables resulting in higher significance when clustered (unsupervised data mining ).

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