# Do Beta weights from regression have error terms?

I am looking at standardized regression weights (i.e., Beta weights). I was thinking of reporting the errors next to the weights in a figure, but upon some thought I was debating whether such errors even exist. I know un-standardized regression weights have standard error parameters, but do standardized regression weights have error terms?

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As with any other statistic, they are random variables, and so have their own sampling variance. It isn't usual to think of them as having an error term (no such term is explicit in the model), but they are estimates of a population quantity - with sampling error and so while it wouldn't usually be expressed that way, could at least arguably be written with an error term. –  Glen_b Apr 17 at 3:49

Yes, they exist.

Are you looking at SPSS output, by chance? (I seem to recall that SPSS uses terminology like you are using.) Here is an image of SPSS regression output that I found on the internet:

The standard errors to the left of the Standardized Coefficients are not scaled properly for what SPSS calls Beta. Instead, those SEs are for the B column at the far left. So, I would not report those SEs with the Beta's.

You can get your own standardized coefficients and corresponding SEs, without relying on SPSS to do it for you. You simply standardize all of your variables ($Y$, and all of your $X$'s) by turning the values into $z$-scores. Then run your regression model with the $z$ transformed variables instead of the raw variables. Now what SPSS reports in the B column will match what it reports in the Beta column and the Std. Error's will be appropriate.

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Haha thank you for the kind words! I can't believe I did not simply think of your solution, thank you. Why are SEs never reported for Beta weights? Is it because they are a bit harder to interpret? –  Behacad Apr 17 at 5:02
Computing the SEs in this way gives you standard errors that are consistent only if the null hypothesis is true. In general, equations that give you proper SEs without having to assume the null are quite a bit more complicated. See the recent article by Yuan and Chan (2011) in Psychometrika (goo.gl/15YahG). –  Wolfgang Apr 17 at 5:36