my understanding is that Multinomial logistic regression is where your dependent variable could take values of 1,2 or 3 where 1-3 are classes. But what isit called if you have two dependent variables your model is supposed to predict continuous values with logistic regression?
for example,I am trying to predict the number of males and number females at an event given a list of conditions [weather,day of week, time of day]
An analysis with multiple dependent variables is called a multivariate analysis. If you had two binary dependent variables, you could perform multivariate logistic regression.
However, your research question doesn't seem to indicate you have binary variables. If my understanding is correct, you have a data set where each entry is an event, and the columns correspond to the predictors (weather, day, time) and the outcomes (number of males, number of females). In this case, you can use linear regression models or count models (e.g., negative binomial), and you can use the multivariate version of these. Count models might be more realistic because your outcome variables are positive integers (i.e., number of males and number of females).
If your goal is prediction and you're not so interested in the individual effects of variables but rather on making good predictions, you can avoid parametric models and use a machine learning method like a random forest or gradient boosting machine. If there are nonlinearities in the relationships between the predictors and the outcomes beyond those included in the regression models, machine learning methods may be better suited to make the predictions for future events.
The two class case is (standard binomial) logistic regression. If you say just "logistic regression" that is what people would assume you are talking about.
If your observations are of only two genders, then you are describing a binomial classifier. If you consider more, you would indeed require a multinomial classifier.
In the binomial setting, you would represent one gender as "not the other gender", and so you would really only be answering one question: is the person gender 1? or are they not? And in that question (and your output score), you're able to classify your observations into two classes.
Multinomial classifiers are a bit more complicated, but can be represented by a series of n binomial classifiers, where n is the number of classes.
