I have a dataset about the functionality of rural water supply points (boreholes etc) and I am undertaking a logit regression. My independent variables of interest are the type of water point (about 5 categories) and the year of construction (1950-2016, so I consider this as a continuous variable). The dependent variable is a boolean (water point is currently functional? yes/no). I could set up dummy boolean variables for my categories and proceed with a logit multiple regression from there.
I understand that multiple regression could be advantageous because it handles covariance of the independent variables (eg this example or this one ). However, it's hard to understand how this sort of thinking applies where one of my independent variables is unordered categorical.
From the above reading, I suspect that multiple regression could take care of an effect such as a tendency to build fewer boreholes (type1) in the last 10 years whilst preference to build wells (type5) has increased - ie, that "year of construction" and "type" correlate to each other. But when I ask my logit model to predict functionality, I have to input both independent variables anyway, to get my prediction out. Why doesn't this wholly take care of said effect?
In this case, where I could easily run 5 univariate logit regressions (one for each type of water point) or otherwise could run a multiple regression using all the available data, what are the conceptual advantages or disadvantages of each approach? Does each method answer a slightly different statistical 'question'? How does the extra data, from waterpoint types 2-5, actually influence the prediction of functionality for waterpoint type 1?