I am taking a statistics course where we are learning about Logistic Regression.
In particular, we are learning about the relationship between the regression coefficients and the Odds Ratio. This article on Wikipedia (https://en.wikipedia.org/wiki/Logistic_regression) provides a good summary: "In simple terms, if we hypothetically get an odds ratio of 2 to 1, we can say... "For every one-unit increase in hours studied, the odds of passing (group 1) or failing (group 0) are (expectedly) 2 to 1 (Denis, 2019)."
I am trying to understand if this example can be extended to compare Odds Ratio for multiple variables.
For example, suppose the response variable is whether the student "Pass or Failed". And suppose we have information on the age, gender, whether the student had a tutor (yes/no) and the number of hours each student spent studying. I think in this case, the general model would appear as : log(p/1-p) = B_0 + B_1X1 + B_2X2 + B_3X3 + B_4X4 . Given the data, I could use some software like R or SAS to fit a Logistic Regression model to this data.
Suppose I am interested in finding out the effect on the odds of passing for each one-unit increase in hours studied for males with tutors vs. females without tutors. It is unclear to me as to how I can adapt the Odds Ratio formula to answer this question (or whether in general the Odds Ratio formula can be used to answer such a question).
Reading online, it seems that one thing I could do would be to create "interaction variables" - that is, instead of recording the gender of each student and whether the student has a tutor or not : I could also record both of these variables together into a single variable (e.g. male with tutor, male without tutor, female with tutor, female without tutor). Then perhaps I might be able to use the Odds Ratio formula as is - however, I am not sure if this approach is suitable.
But in any case, could someone please comment on how the Odds Ratio formula can be modified to calculate multiple comparisons?