I am having some conceptual difficulties in understanding and interpreting interaction terms (between a dummy and a continuous variable) in OLS regressions. I was hoping someone could help me out. I know there are similar questions that have been posted, but I wasn't quite sure I understood the answers there.
Let’s say we have an equation where an individual’s years of schooling is the outcome, and we have the individual’s parental income (a continuous variable) and the individual’s gender (=1 if male) as controls. And we want to see whether parental income has a differential effect by gender. So the equation would be as follows:
YearsofSchool = β0 + β1 ParentIncome+ β2 Male+ β3 ParentIncome * Male + ε
I understand that β1 denotes the effect of parental income on schooling for females, and β1+ β3 for males. So, for example, if β1 is significant, we can say that parent’s income is significantly associated with schooling of girls. Similarly, we test for the significance of β1+ β3, and conclude whether or not income has a significant association with schooling for boys.
However, what I don’t understand is how to interpret the coefficient on the interaction term, β3. What does β3 denote in this case and how should we interpret it? E.g., if we find that parental income is significantly associated with schooling for girls only, but the interaction term is insignificant, what would that mean?
I look forward to your help.