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I am interested in understanding the specific relationships between an dependent variable (low birthweight), which is binary and various independent variables (which are also binary). So far, the way I have been doing the logistic regression is to run the regression with low birthweight and all of the independent variables.

My question is: Is running the regression with all of the variables the same as running the regression with each independent variables one by one? I ran both of them (one by one, and all at once) and I received different coefficients. So which one is more accurate?

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    $\begingroup$ Welcome to CV. Since you’re new here, you may want to take our tour, which has information for new users. No, they are not the same. When you have multiple predictors, the coefficients are partial (I am sure you heard the expression: "holding all other variables constant"). Which one is more accurate? It depends on your aim. If you want to control the effect of some variables while estimating the effects of others' (which is most probably the case), you should include all these variables in the model. $\endgroup$ – T.E.G. - Reinstate Monica Dec 13 '17 at 0:42
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    $\begingroup$ I recommend reading this question (and answers) to get a better idea about control: stats.stackexchange.com/questions/17336/… $\endgroup$ – T.E.G. - Reinstate Monica Dec 13 '17 at 0:44
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(This is not specific to logistic regression; it is true of any kind of regression model.)

Both are presumably accurate. But they give an accurate answer different questions, so it shouldn't be surprising that the answers differ. In general, regression models do not estimate the direct association between a covariate and a response unless the units (e.g., patients) were randomly assigned and the levels of the covariate were independently manipulated (i.e., the data are drawn from a true experiment). If the data are from a true experiment, the coefficient from the treatment variable should be (approximately) the same in both the simple regression model and the multiple regression model.

In any model, for any variable that was not independently manipulated and randomly assigned to the study units, the coefficient is an estimate of a marginal association. The only question is which marginal association is being estimated. There are potentially infinite margins to consider. You need to decide which you care about and why.

For a clearer sense of the relevant issues, there are a few of my existing answers that may be helpful:

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