Assessing spurious effect of a third variable on the relationship between a response and a predictor Say, I have a biomarker that is strongly associated to a gene. This biomarker is also strongly associated to another trait, like glucose, but the gene is not. 


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*If I perform a regression between the glucose and biomarker + gene I get the biomaker and gene both significant: Is this a spurious effect? 

*And what if I add an interaction term between the biomarker and gene on the glucose (biomarker*Gene+Gene+biomarker) and all the terms are significant? 


What does it mean if when I add a third variable (biomarker) in the regression the second (gene) becomes significant all of the sudden? Does it mean that the second variable is then significantly associated with the dependent?
 A: The most likely explanation is that the Biomarker is a suppressor variable.  A suppressor variable is correlated with another predictor variable in such a way that the predictor is significant when both are entered into a model, but not when it is entered alone.  Unfortunately, suppression is just one of those statistical phenomena that aren't very intuitive.  This website is fairly long, but very clear and includes a discussion of all the relevant issues with a section on suppressor variables at the end.  I also found this American Statistician paper, which is specific to suppressor variables.  I haven't read it yet, but it looks quite good.  
Another possibility is that the Biomarker is not a suppressor, but it accounts for enough of the residual variance in your response variable (glucose), that the weaker gene - glucose relationship becomes significant.  Remember that 'significance' is assessed by the relationship between the variability that a predictor accounts for, and the residual variability.  If the Biomarker accounts for a good deal of what would otherwise be residual variability, but consumes only, for example, 1 degree of freedom, this could increase the power of your analysis with respect to the gene.  Under this interpretation, you would have simply needed more data to resolve the gene - glucose relationship, but there might not be any correlation between the gene and the Biomarker.  
In neither case would it be correct to call this a spurious correlation.  A spurious correlation is when there is a zero-order correlation between two variables, but no direct relationship.  The classic situation is where two variables A and B are both caused by a third variable, C, but otherwise have no direct connection.  A real-world example I once heard is that when the economy speeds up, it enhances both the birth rate and steel production, but that there is no direct connection between them.  
An interaction is a third, distinct concept.  An interaction obtains when you would describe a situation using the word 'depends'.  For instance, if someone asked what is the effect of taking the birth control pill, you might say:  

It depends, for women, it suppresses ovulation and so reduces the
  chance of pregnancy.  But for men, since they don't ovulate, it has no
  effect.  

(I acknowledge that this is a rather forced example.)  
