I have a dataset where each row corresponds to a country and contains independent variables such as "per capita income" and "mean education status." Additionally, there are two variables of interest: "number of restaurants" and "number of restaurants with Michelin star."
Our goal is to predict the ratio of "number of restaurants with Michelin star" to the total "number of restaurants" using the independent variables "per capita income" and "mean education status." However, it's important to note that the number of restaurants varies significantly among countries, ranging from as low as 3 to over 100. This raises the question of whether we should consider weighted regression based on the number of restaurants.
Given that both the numerator and denominator are count variables, What is the true regression model that i should use?