# Comparison of Coefficients of two different Regression Models

#### LariB

##### New Member
Hi everyone,

I am analyzing the impact of price and promotion activities on sales in two separate 2-Way-Fixed Effects models. One model is for private labels, the other for national labels.

I now want to compare the coefficients of the two models with each other. My goal is to be able to state which type of price and promotion activity has a stronger effect for which brand.

Can anyone suggest an appropriate method? For linear models I found the Chow Test.

Thank you very much in advance"

#### mmercker

##### New Member
So your goal is to say if two regresson coefficients are significantly different? If so: you have from both regression models the coefficient (beta) and the standard error of this coefficient (se). Assuming that the distribution of the betas is approximately normal (e.g., if both regression analyses rely on more than 30 samples) you can calculate it in R in the following way using a z-statistic:

SE <- sqrt(se1^2+se2^2) #that is the approximate standard error of the difference
z<-(beta1-beta2)/(SE) #that is the z-transformed difference
p <- 2*pnorm(-abs(z)) #that is the p-value

#### katxt

##### Member
Is the data suitable for combining into a 3 way model with private/national as a factor?

#### rogojel

##### TS Contributor
hi,
could you merge the two datasets, add a discrete variable for label type and anlyse it this way? It would provide all the info you need and some more if you check interactions as well.

regards

#### noetsi

##### Fortran must die
I believe, although its been a long time, that there are problems in comparing across data sets with different distribution (which has been suggested above). Are you using the same data set to build both models, or different data sets.

I think merging the data with a private/public dummy makes more sense. You might find an intervention effect so that the regression model is different for private and public units.