Google Interview Question: If each of the two coefficien... | Glassdoor

## Interview Question

Quantitative Analyst Interview

# If each of the two coefficient estimates in a regression

model is statistically significant, do you expect the test of both together is still significant?
Answer

## Interview Answer

6 Answers

1

A multiple testing problem.

Anonymous on Feb 7, 2015
1

"beta1 !=0 AND beta2 !=0" implies "beta1 !=0 OR beta2 !=0"

so should expect still significant

JG on Nov 29, 2015
0

Yeah I think maybe they actually asked about the converse

Anonymous on Apr 2, 2016
3

When you test them together, and you look at the p values individually, then they may not still be significant because of collinearity problem. However, if you look at the full model, it should have more explanatory power than either of the two reduced models.

mx on Sep 9, 2016
1

When you test them together, and you look at the p values individually, then it's possible that one or both is not significant because of collinearity problem. However, if you look at the full model, it should have more explanatory power than either of the two reduced models.

mx on Sep 9, 2016
2

This can occur when the estimators of the two coefficients are correlated. You don't even need to have collinearity. You can see a detailed counterexample in the response here:

http://stats.stackexchange.com/questions/151403/significance-of-individual-coefficients-vs-significance-of-both

So yes, there are counterexamples, but usually when both tests are significant then the joint test is also significant. So I would expect the joint test to be significant. That said, I would ask them to clarify the wording of the question to see whether they were asking for a counterexample.

This is a pretty hard question if you don't happen to already know the answer. I'm preparing for my interview right now, and I'm hoping they won't ask something like this.

Anonymous on Nov 27, 2016

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