Timeline for How are partial regression slopes calculated in multiple regression?
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10 events
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| Oct 14, 2015 at 7:04 | comment | added | hans0l0 | Is there any lazy man's way to plot these slopes, without computing all those manually? | |
| Dec 1, 2013 at 5:09 | comment | added | jay | Yes that makes sense thanks. We got there in the end! | |
| Nov 28, 2013 at 14:57 | comment | added | Alecos Papadopoulos | No problem Jay... try this: informally, residuals are "what is left unexplained". The X2~X1 residuals is what of X1 is not explained by X2. Now consider the Y~X2 residuals. These reflect what part of Y is not explained by X2 (and therefore is explained by X1 and by the error term). So even if you regress the original Y on the X2~X1 residuals, these will only explain that part of Y that is left unexplained by X2. So by using Y~X2 as the dependent variable, you "remove" only that part of Y that is explained by X2- leaving unaffected that part of Y that is explained by the residuals X2~X1. | |
| Nov 28, 2013 at 7:14 | comment | added | jay | I've read through it multiple times and I'm afraid no, don't get the intuition. I appreciate you taking the time to write out such a detailed explanation...it's just not in a language that I understand. | |
| Nov 25, 2013 at 8:42 | comment | added | Alecos Papadopoulos | "The three models give mathematically identical results" means that either way you will obtain the exact same result. Can you get the intuition as to why? | |
| Nov 25, 2013 at 3:38 | comment | added | jay | Thanks for that in depth answer...which unfortunately has gone way over my head! At this stage I'm after a more conceptual cf mathematical understanding - ie is the partial slope of X1 in a model also containing X2 found by partialling out effects of X2 on X1 AND partialling out the effects of X2 on Y, or just by partialling out the effects of X2 on X1? Cheers | |
| Nov 25, 2013 at 3:20 | history | edited | Alecos Papadopoulos | CC BY-SA 3.0 |
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| Nov 25, 2013 at 3:08 | history | edited | Alecos Papadopoulos | CC BY-SA 3.0 |
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| Nov 25, 2013 at 2:50 | history | edited | Alecos Papadopoulos | CC BY-SA 3.0 |
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| Nov 25, 2013 at 2:45 | history | answered | Alecos Papadopoulos | CC BY-SA 3.0 |