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1)

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)

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) = β

Thanks for explaining!

**"In regression models, there are two types of variables:**

X = independent variable

Y = dependent variable

Y is modeled as random.

X is sometimes modeled asX = 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 = β**

If X is random, E(Y|X) = β

If X is fixed, E(Y|X=x) = β_{0}+ β_{1}X + εIf X is random, E(Y|X) = β

_{0}+ β_{1}XIf X is fixed, E(Y|X=x) = β

_{0}+ β_{1}x"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) = β

_{0}+ β_{1}X 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!

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