# Why do regression coefficients change when excluding variables? [duplicate]

Possible Duplicate:
How exactly does one “control for other variables”?

In my linear model fitted.model <- lm(spending ~ sex + status + income, data=spending), my results were as follows:

Coefficients:
Estimate  Std. Error t value   Pr(>|t|)
(Intercept)    22.55565   17.19680   1.312   0.1968
sex         **-22.11833**  8.21111  -2.694   0.0101 *
status          0.05223    0.28111   0.186   0.8535
income          4.96198    1.02539   4.839 1.79e-05 ***
verbal         -2.95949    2.17215  -1.362   0.1803


Now, when I held sex and all other predictors constant in new lm model mydata<-lm(spending ~ sex, data=spending) my coefficient was

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)   29.775      5.498   5.415 2.28e-06 ***
sex        **-25.909**    8.648  -2.996  0.00444 **


Questions: Should the sex value of -22.118 be the same in my new model? Because I now get -25.909. Since I am holding all constant, I should get a different value, please clarify?...

• Your two models appear to involve two dataset names, dataset and spending. If the data differ, then of course you should expect the results to differ! Please, then, explain the relationship between those two datasets. – whuber Sep 14 '12 at 16:18
• Even if the same data (response variable values) are used in two models removing covariates could change coefficients simply because a covariate removed is correlated with one that remains. I believe that this can be avoided if the covariates can be constructed to be orthogonal such as with orthogonal polynomials. – Michael R. Chernick Sep 14 '12 at 16:49
• Actually the data set is the same, spending. I typed the wrong name of the dataset. I needed to determine the difference in predicted spending for a male vs. a female with other variables held constant. But i was questioning if the value of the sex in my 1st model using all constants should be the same value when one variable and all other constants. – MsSnowy Sep 15 '12 at 1:07
• Your question is related to this CV question: How exactly does one "control for other variables"?. It is explained why regression coefficients change when we include other variables (which is also referred to as "controlling for"). – Bernd Weiss Sep 15 '12 at 3:03
• @berndWeiss Good reference to a duplicate or near duplicate. I gave an answer to the OPs specific question but the responses in the link should give the OP a deeper understanding of what is going on and what the issues are. Maybe it would be appropriate to close this question. – Michael R. Chernick Sep 15 '12 at 3:38