topic Re: Total effect of main variable including it's interaction with dummy in Statistical Procedures

Total effect of main variable including it's interaction with dummy

MAC1430 — Tue, 25 Aug 2020 00:47:56 GMT

I am going to estimate the following model:

y=constant+b1(X)+b2(X)(Dummy)

We have daily data from 1990 to 2000. Dummy variable is equal to one for the daily data of year 2000, else zero. b1 is the main effect, and b2 is the marginal effect because of the dummy. The total effect in year 2000= b1+b2. How to estimate the statistical significance t-stat for this total effect (b1+b2)?

One and easy way is to use a a dummy with $D^{'} = 1 - D$

$D^{'} = 1 - D$

Re: Total effect of main variable including it's interaction with dummy

PGStats — Tue, 25 Aug 2020 00:56:35 GMT

The statistical significance of b2 (i.e. the probability that hypothesis b2=0 can be accepted) will tell you if the relation between y and X has changed in 2000, compared with the 1990-1999 period.

Re: Total effect of main variable including it's interaction with dummy

MAC1430 — Tue, 25 Aug 2020 01:04:18 GMT

Thank you. But I am interested in the total effect of b1 and b2. The total effect of b1 and b2 is just the sum of b1 and b2, but the issue is how to estimate the statistical significance of the total effect (b1+b2)?

Re: Total effect of main variable including it's interaction with dummy

PaigeMiller — Tue, 25 Aug 2020 11:40:05 GMT

The question you are asking is answered by the overall F-test.

Re: Total effect of main variable including it's interaction with dummy

MAC1430 — Tue, 25 Aug 2020 20:41:14 GMT

Sorry, I should have mentioned it. Yes I am using proc reg. I used test but it provided F-test instead of t-test.

Re: Total effect of main variable including it's interaction with dummy

PaigeMiller — Tue, 25 Aug 2020 20:50:52 GMT

You don't need a t-test, the overall F-test is the exact test you want. And if you could figure out the right t-test to do here, it should give the exact same p-value as the overall F-test.