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I have only discrete independent variables (gender, religious affiliation etc) and continuous dependent variables. Is it possible to use a regression model?

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Yes, though you will want to convert the categorical variables into dummy/indicator variables. Most statistical packages will do this for you as long as it is clear that they are categorical.

Technically when all predictors are categorical you are doing ANOVA, but since many of the statistical packages use their regression code to do ANOVA anyways, it does not matter. If you design your dummy variables appropriately then the regression approach can give more insight than a simple ANOVA fit.

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    $\begingroup$ It might help to clarify the distinction b/t discrete variables & categorical variables for the OP. $\endgroup$ Sep 30, 2014 at 17:57
  • $\begingroup$ Just a note to add to @greg snow's response: Most (if not all) statistical packages will make these dummy codes for you. Certainly SAS, R and SPSS will $\endgroup$
    – Peter Flom
    Sep 30, 2014 at 18:57

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