Two quant interview questions (one stat, one programming) - need help!!!

In statistics, linear regression refers to an approach for modeling the relationship between a scalar response variable and one or more explanatory variables.
a) How would you construct a small data set (less than 50 data points) with 2 explanatory variables, such that both explanatory variables and the response variable are Gaussian, but the residual of the linear regression is not Gaussian?
b) How would you construct a small data set (less than 50 data points) with 2 explanatory variables, such that neither the explanatory variables nor the response variable is Gaussian, but the residual of the linear regression is Gaussian?

programming-solved!

Comments (4)

 
Dec 6, 2016 - 9:34am

Thank you for the useful information!

 
Best Response
  • Principal in HF - Event
Nov 29, 2016 - 11:25pm

I think (a) is impossible (since the sum of gaussians is gaussian) and (b) is trivial - make X and Y be your two explanatory variables with U(-1,1) distributions and make Z (response variable) = X + Y + G (where G is a gaussian deviate with 0 mean and 1 std dev)

Then again it's been a while since I did real quant stuff so I may be missing something obvious here.

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