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| Regression vs. correlation (ON vs. WI... |
 
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Why do the following two models (random example) produce different results for the relationship of Y and X?
MODEL 1:
Y WITH X;
Y WITH Z;
X WITH Z;
MODEL 2:
Y ON X;
Y ON Z;
X WITH Z;
In case it matters, I'm using type=complex; in order to control for stratification. I didn't see any obvious differences for how ON vs. WITH are computed in the UG.
Thank you very much. |
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| Model 2 regresses y on 2 covariates x and z. This means that the correlation (assuming unit variances for all variables) between y and x is not the same as the regression coefficient for y on x. |
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