Where X is a regressor and Y is the dependent variable. I know that if E[XY]=E[X]E[Y] then X and Y are independent, hence uncorrelated but I don’t get what E[XY]=0 means.
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$\begingroup$ A bit more context would help. Is $E[XY]=0$ an assumption or a result? The same goes for $E[Y]=0$. $\endgroup$– Herr K.Jun 16 at 15:53
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3$\begingroup$ If $X$ and $Y$ are independent then $E[XY]=E[X]E[Y]$ but not conversely. $\endgroup$– BertrandJun 16 at 16:37
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$\begingroup$ Yes sorry, I made a mistake and it’s not E[Y]=0 but, again, E[XY]. Also, exactly, E[XY]=0 is an assumption. $\endgroup$– tryingtogetsmthJun 16 at 22:02
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I think this is a very fundamental confusion. $E[XY]$ means that the result of $X*Y$ should average together to be 0. Relevant operators are $E()$, which is average.
Implications can be very far reaching, but most notably is that (as mentioned above) if $E[XY] \neq E[X]*E[Y]$ then $X$ and $Y$ are not independent. It is a good mental exercise to attempt to see if you can construct a minimal working example of variables that are independent or dependent.
