I just have a question about if chi square test for the association say between two variables (I think both are discrete in this case) in a 2 by 2 table says anything about what "model" is used in the analysis.
I know that for example if you have a continuous response variable (say BMI index), and say another continuous variable (say age). And if we assume the relationship is linear, then we could fit a linear regression to the data between these two variables right? and the linear regression is called a "model", is that correct?
But say if we have a 2 by 2 table for two discrete variables, and we want to see if there is any association. I think we use a chi-square test right? in this case, do we say we have a model for these two variables? I was reading somewhere that this can be considered a logistic regression model, is it correct?
My question is, when we say a "model", is it correct that we are saying the observed data are being generated by the model? So in a linear regression, we are saying the response variable is being generated by a linear mechanism and it is linear related to another variable, is it correct?
So for a two by two tables, can we also say the same thing? Can we say we have a "model"? If I am a statistician, and someone approaches me and say "how do we find out if there is association between these two discrete variables in the data, what "model" should we try?" , is there actually a "model" in this case? is there a generating mechanism like a linear regression?
Thank you for your time