comparing regression coefficients among many groups

#1
Hi all, first of all, sorry for my poor English since I'm not native English speaker,


I have this simple OLS regression equation model with one independent variable X and one dependent variable Y... Y= a + bX

now I want to find out if there is difference in the regression coefficients (b) among several groups..

If the number of groups is small (e.g. male and female), then I would add interaction variable of the group and the independent variable x,

but since the number of groups is 25 (all categorical, since they are name of cities), I don't know what to do! should I make 24 dummies and add 24 interaction variable between those dummies and independent variable X? T_T

what statistical method can i use now? please help me. Thank you very much!
 
#2
IMO you should create some new variables using content analysis, separating the cities into only a few categories on the basis of a series of dimensions which have theoretical meaning in the context of Y.

For example (I have no idea what Y is, but this should convey what I speak of), some content-coded binary dimensions might be: per capita income (above or below median for this value for all 25 countries); median age of death (above or below median for this value for all 25 countries); calories consumed per day (above or below median for...), and so forth.

In this way the chaotic 25-category variable is turned into easily interpreted, quickly analyzed, theoretically justifiable binary indicators (logistic regression) or dummy variables (multiple regression). And, binary variables are easiest to use when studying interactions.