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I have a situation where two variables when entered into a regression model independently, both predict a third variable, but when I entered both those variables into the model together, neither one significantly predicts the third variable independently, but overall the model is significant.

In other words.

1st regression - A significantly predicts C

2nd regression - B significantly predcits C

3rd regression (both entered together):

  • A does not significant predict C
  • B does not significantly predict C
  • Model overall is significant

What does this mean? Does it just mean they share too much variance (A also significantly predicts B)? How would I interpret this?

thanks



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  • $\begingroup$ I think you will find the information you need in the linked thread. Please read it. If it isn't what you want / you still have a question afterwards, come back here & edit your question to state what you learned & what you still need to know. Then we can provide the information you need without just duplicating material elsewhere that already didn't help you. $\endgroup$ – gung - Reinstate Monica Aug 17 '17 at 15:50
  • $\begingroup$ Thanks, I think this may explain what is going on with my data well. However, this leads me to a follow-up question about mediation. As it is a different question, I will start it in a new thread. $\endgroup$ – neij Aug 17 '17 at 16:10
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This is very normal.

See this question and answer

Two negative main effects yet positive interaction effect?

Similar, suppose, your $A$ is amount of hot water, $B$ is amount of cold water, $C$ is number of death for fish. Both $A$ and $B$ can contribute $C$ significantly, but adding both $A$ and $B$, $C$ may have no impact.

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  • $\begingroup$ Thanks for your answer, that make sense. But is it always the case that a significant overall effect of a model is the result of an interaction when the individual predictors are not significant? $\endgroup$ – neij Aug 17 '17 at 16:09

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