Chow test to compare regression models with different parameters


New Member
Hi, I have some questions about chow test. Let’s say what I am doing is:

I have a set of house sale data (n = 30000) and somehow I divided it into two subsets (n1 = 10000 and n2 = 20000). Using house price as dependent variable and a long list of housing attributes as independent variable, I got a regression model for each of the subsets, with stepwise variable selection:

Subset 1: house price = 5*(number of rooms) + 2*(size of garden) + 3*(distance to school) + 2*(air quality) + 500
Subset 2: house price = 4*(number of rooms) + 3*(size of garden) – 6*(crime rate) + 600

I need to test if the two regression models are significantly different.

Nearly all the examples of chow test I found online compared two models with the same parameters, except in a research paper ( The equation used in that paper (shown in the attached image) is slightly different from the standard one to account for the difference in number of parameters of the two models.

Further, not only the numbers of parameters might be different, but what specific parameters are used in each of the models might also be different. I feel many housing market studies used chow test to compare price/regression models of different markets, however, they did not make it clear that they were comparing models with different parameters, or they simply didn’t give what equations they used exactly.

So my questions are:
1. Can we test if two regression models are different using chow test when the models are already "very different" with different parameters?
2. If not, should I run regression with forced entry instead of stepwise entry to ensure the two models have the same parameters for the comparison purpose?

Thank you very much!