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!
This is a good question. Check out this post, it should help explain why this is case. I can't really explain this concept much better than the people here did.
http://stats.stackexchange.com/questions/12262/what-if-residuals-are-no…
Thank you for the useful information!
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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