# Symmetrical regression

Ordinary least squares regression is clearly not symmetrical! Regressing $Y$ on $X$ is not the same as regressing $X$ on $Y$. What kind of regression is symmetrical?

I have 5 variables ($A$, $B$, $C$, $D$, $E$) and I want to find out the true relationship among the variables. $$W_a * A + W_b * B + W_c * C + W_d * D + W_e * E + W_0 = 0$$ where ($W_a$, $W_b$, $W_c$, $W_d$, $W_e$ and $W_0$ are constants).

Is Deming regression symmetrical?

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CV won't let you upload images if your rep is too low. If the image exists somewhere else on the internet, you can post a link to it in a comment & a higher-rep user can edit your question & add the image for you. You seem to already get the idea about y~x vs x~y, but you may still benefit from reading my answer here, this question may also be helpful to read. –  gung Jul 28 '12 at 13:48
Ordinary least squares regression with a single response $Y_i$ and single predictor $X_i$ is not symmetrical in terms of the estimates, of course, but the $p$-values on the slopes and the $R^2$ should be identical. –  Macro Jul 28 '12 at 13:49
@gung Well, I have only one account and I posted under one account. Yesterday's question was very confusing. That's why I rephrased and simplified the question to attract more answers. –  user1437139 Jul 28 '12 at 14:11
Sorry, my mistake about the accounts. It's better to edit / update your question, than to re-ask it. You should probably delete the one you don't want, or edit them to make them distinct. If you want the image posted, can you put it on the internet somewhere & post a link in a comment here? –  gung Jul 28 '12 at 14:23
Answers can be found under the errors-in-variables tag and the pca tag. –  whuber Jul 28 '12 at 15:45
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