1) "In regression models, there are two types of variables: X = independent variable Y = dependent variable Y is modeled as random. X is sometimes modeled as random and sometimes it has fixed value for each observation." I don't understand the meaning of the last line. When is X random? When is X fixed? Can anyone illustrate each case with a quick example? 2) "Simple linear regression model: Y = β0 + β1X + ε If X is random, E(Y|X) = β0 + β1X If X is fixed, E(Y|X=x) = β0 + β1x" Now what's the difference between E(Y|X) and E(Y|X=x)? The above is suuposed to be dealing with 2 separate cases (X random and X fixed), but I don't see any difference... Most of the time, I am seeing E(Y) = β0 + β1X instead, how come??? This is inconsistent with the above. E(Y) is not the same as E(Y|X=x) and I don't think they can ever be equal. Thanks for explaining!