I did a simple regression where the independent variable was the educational background of the mother. The dependent variable was the language skills score of the child.
I switched them around and did another regression to see which coefficients change and which didn't.
The t-test of the gradient was the same for both regressions. I find it difficult to explain why that is the case. The b-value and the standard error, the values that I need to calculate the t-test, were different for each regression. It puzzles me how dividing a different b-value by a different standard error gets the same outcome.
Edit: I have a related but different question now. If I standardize the two variables, so turn them into z-scores, what would the value of the intercept be? I have no idea how to calculate this. I don't see the relation between z-scores and the intercept. Maybe the answer is quite simple but I have to admit that learning about z-scores was a long time ago so maybe I'm missing something very obvious.