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Will running multiple regression including 2 independent variables give the same output for each independent variable if we run linear regression using the same independent variables separately/individually?

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    $\begingroup$ ... have you tried it? $\endgroup$ – Matt Parker Mar 21 '12 at 16:03
  • $\begingroup$ Yes I have tried it before posting here....just wanted to have a double check on what i am thinking is correct or not... $\endgroup$ – Shantanu Mar 21 '12 at 19:35
  • $\begingroup$ Okay! Sorry to ask, then, but you'd be surprised how often people ask questions that could be answered by just doing it. Double-checking your thinking is always welcome! $\endgroup$ – Matt Parker Mar 21 '12 at 20:39
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The short answer is "No".

The longer answer is "Only if the 2 independent variables are orthogonal", but that is only true of the parameter estimates, the variance and standard error estimates will still be different. The only case where everything will match is when all 3 variables are orthogonal (so there is no relationship at all).

Another longer answer is "Why not try it for yourself?". Just get some real data, or textbook data, or generate your own random data and run the 3 regressions and compare them. Do this for different datasets with different relationships and you will quickly see that the slope estimates change.

Another thing to try is to do the regression with both x variables, then do the individual regressions and also regress x1 on x2, then regress the residuals from y vs. x1 on the residuals from x2 vs. x1, then compare that estimate to the slopes from the full model.

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  • $\begingroup$ Thanks for your response. I did it myself what you suggested and also had the same opinion. Just wanted to double check on it. That helps...thanks.. The independent variables could be inter correlated to each other which could give different results. $\endgroup$ – Shantanu Mar 21 '12 at 19:34

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