Interaction terms

Someone comments, "I'm a little confused on how we use interaction variables for our regression. For instance, if our interaction variable is oxen * ethnicity, how do we interpret the numbers this gives us (since the value attached to ethnicity, 1,2 or 3, is just an arbitrary number used for organizational purposes)? Or something like birth group * married?"

You are right- if you leave ethnicity with multiple categories there is no possible interpretation (even without interacting)! it doesn;t mean anything to be ethnicity 2 and go to ethnicity 3, or to go from ethnicity 500 to 560.

So the ethnicity variable has to be recoded to be a dummy variable- 1=bwa, 0= non-bwa, for example. Then this dummy variable can be interacted (i.e. multipled) by the oxen, to create bwa*oxen.

Then if the regression were y = a + b*bwa + c*oxen + d*oxen*bwa,

the effect of more oxen on outcome y would be
c - for non bwa
c+ d - for bwa households

in other words, the slope differs for the two different groups.