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 $

  • 2
    $\begingroup$ @Glen_b are you putting the dependent variable on the right hand side? Typo or maybe I'm confused:)? $\endgroup$
    – KOE
    Feb 17, 2014 at 9:10
  • 1
    $\begingroup$ @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.] $\endgroup$
    – Glen_b
    Feb 17, 2014 at 12:18

1 Answer 1


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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