Skip to main content
Cross Validated

You are not logged in. Your edit will be placed in a queue until it is peer reviewed.

We welcome edits that make the post easier to understand and more valuable for readers. Because community members review edits, please try to make the post substantially better than how you found it, for example, by fixing grammar or adding additional resources and hyperlinks.

Required fields*

4
  • $\begingroup$ First, it's not "necessary", it depends what you intend to do. There are some good answers, but I think the crux is the underlying assumption of causality, in the sense of the Xs "causing" the y, and if you look at it that way you see that the distribution of y is "caused" by the distribution of the rhs, which is to say the Xs and the errors (if any). You can do plenty of econometrics with very limited distributional assumptions and, in particular, without normality. Thank God. $\endgroup$ Commented Jan 28, 2014 at 20:54
  • 3
    $\begingroup$ $\hat y$ is not $X\beta$, and the population mean of the $y$'s isn't the same as the sample estimate of it. Which is to say that the second thing is not actually the same thing as the first, but if you replace it with its expectation ($E(\hat y) = E(y) = X\beta$), the two would be equivalent. $\endgroup$ Commented Jan 28, 2014 at 21:36
  • $\begingroup$ What is $\hat{y}$? And if $y_i$ varies with $i$, why doesn't $X\beta$ vary? Please make up your mind which notation you want to use, the vector or matrix. Now if we assume that $\hat{y}=X\hat\beta$ your notation is more than bizzare: $y_i\sim N(x_i'(\sum x_jx_j')^{-1}\sum x_jy_j,\sigma^2)$, i.e. you define distribution of $y_i$ in terms of itself and all the other observations $y_j$! $\endgroup$ Commented Jan 29, 2014 at 8:26
  • 1
    $\begingroup$ I've downvoted the question because I think the notation is confusing and this already resulted in several subtly conflicting answers. $\endgroup$ Commented Jan 29, 2014 at 8:31