It is possible to obtain a negative beta value in regression analysis. However, the interpretation differs depending on the type of regression you are fitting (linear, logistic e.t.c)

Stepwise selection selects by statistical significance of the betas, not by their sign.

However, you should always be very careful interpreting the result of a stepwise selection. This procedure has many drawbacks, one of which is that the remaining variables often considerably over-estimate the correlations. It is very likely to come up with an entirely different result/model if you'd repeat the experiment, so anything you conclude from this one result may not at all generalize. This risk is way bigger than one may think as by the (small) reported p-values, particularily if there are many variables to select from.

There are better tools for model selection (e.g. lasso), but they all share the problems in principle and to some extend. The best way to build a model is to delibartely define the variables (and their interactions!*) that should be modelled based on theoretical considerations and understanding of the subject matter problem.

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* I note this especially because the stepwise selection uses only what you start with, and in many cases people start with simple linear combinations, completely ignoring the possibility of non-linear relationsships and interactions between variables (for good reasons, too**). If, for instance, an interaction plays a role (and this is quite often the case), the stepwise procedure will run into a combination of variables that accidentally and somehow compensate that interaction. So eventually you miss the relevant relationships and are up to interpret spurious relationships instead.

** starting with all possible interactions of all possible orders and all possible at least polynomial relationsships up to some degree will give myriards of possible models and you will always get some final model with a few nice highly siginificant variables, no matter if there is really some relationship present or if you start with pure noise.

@Hugo

Stepwise regression is nothing but Multiple Linear Regression putting each Independent variable in a separate model successively while regressing them on the dependent variable. Beta coefficients are meant for predictive power of respective IVs to DV and nothing different from Multiple Linear Regression.

Thank you all!