Logistic regression is a type of regression which is used when the dependent variable is categorical. The DV can be dichotomous, ordinal or nominal. But there are several reasons why using OLS regression with any categorical DVs is a bad idea:
1. It violates the assumptions of the model (residuals will be heteroscedastic and nonnormal).
2. The OLS model makes nonsensical predictions, for example, predicting that people are halfway between dead and alive.
3. For nominal DVs, the coding is completely arbitrary, and for ordinal DVs it is arbitrary up to a monotonic transformation. Yet recoding the DV will give very different results.
Logistic regression deals with these issues by transforming the DV. It uses the log of the odds ratio of being in a particular category for each combination of values of the IVs. The odds is the same as in gambling. The ratio of the odds allows us to consider the effect of the IVs. We then take the log of the ratio so that the final number goes from −1 to 1, so that 0 indicates no effect, and so that the result is symmetric around 0, rather than 1.