# Adding coefficients to obtain interaction effects - can I add standard errors?

I posted this question earlier and am rewriting it in hopes of getting some guidance. I am using a weighted regression (after propensity score matching) to obtain estimates of the effects of a treatment (treat) on an outcome for different income quintiles. I include interactions of the quintiles and the treatment in the equation, as shown below:

regress outcome treat quintile2 quin3 quin4 quin5 treatXquin2 treatXquin3 treatXquin4   treatXquin5


To obtain the effect of treatment on quintile2 I add the coefficient on treat with the coefficient on treatXquin2. However, what do I do with the standard errors? Can I simply add the standard errors on the two coefficients together? Can I add the t-stats together?

Any advice would be much appreciated. I'm not a stats expert but have a basic understanding of econometrics.

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Please explain why you're not satisfied with suncoolsu's answer to your previous version of the same question stats.stackexchange.com/q/3653/449. Also please indicate what software the code in your question is for, and add an appropriate tag. That way, someone with experience in that software package might be able to suggest explicit code. – onestop Oct 18 '10 at 14:52
Sorry for posting a second question. For some reason I can't figure out how to edit my question. I'm new to the site so please bear with me. And thanks again to those who have provided answers so far! – Sarah Oct 18 '10 at 15:15
You can edit the question by clicking 'edit' which appears below the tags for your question. If some aspect of suncoolsu's answer is not clear you should ask for clarification via commenting to the answer. There is a 'add comment' link below every answer. – user28 Oct 18 '10 at 15:49
Thanks Srikant. I appreciate your help. – Sarah Oct 18 '10 at 15:57