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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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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