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This is a very basic question, but I haven't been able to get an answer with my google-fu.

In the following sentences:

We regress W on Z

We performed a regression of W on Z

I'm unsure what of and on denote. Do I read that as:

$W \tilde{} \alpha + \beta Z + \epsilon $


$Z \tilde{} \alpha + \beta W + \epsilon $

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Thanks for that, I thought that would be the case. – Manetheran Feb 17 '14 at 0:35
@Glen_b are you putting the dependent variable on the right hand side? Typo or maybe I'm confused:)? – Student001 Feb 17 '14 at 9:10
@Karl Uh, yes exactly, that's a typo. Try again! ... Both phrases have W on the left (dependent variable, response variable, y-variable) and Z on the right (independent variable, predictor variable, x-variable). [I realize this pretty much duplicates the answer, but I wanted to explicitly confirm that this is the case.] – Glen_b Feb 17 '14 at 12:18
up vote 7 down vote accepted

The "regression of W on Z" means you're predicting W from Z. Using your equations, this corresponds to the first one, namely $W=\alpha+\beta Z+\epsilon$

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