I am conducting a regression analysis and my aim is to see whether a theoretical approach applies to the data. The data of the dependent variable is seperated to three categories. Therefore, I have 1 of them as referrence and added 2 dummy variables.

So, before looking at data, I expect one of my dummy variable to have a negative coefficient, the other to have positive coefficient. These expectations are due to the theory which I am trying to test with data.

My question is whether I can consider the significance tests of the dummy variables stated above as one sided or not.

>Solution :

So, the question essentially is whether the assumption that

dummy1 * dummy2 < 0

is premature or not. Cases:

We know that it is the case

In this scenario it is correct to assume that, but you also need to make sure that your software properly validates new input and fixes old data that would violate this rule.

We do not know whether that’s the case, but we know that it should be the case

In this scenario your assumption is premature if you do not have a test and data validation for dummy1 having a different sign from dummy2. If you have validation/test/fixes and you do not have counter-examples, then it seems not to be premature.

We only have the theory

In this case this is premature until it is proven either mathematically or via engineering means.