I have been given yearly salaries for two people (A and B) for $40$ years. How could I use linear regression to test whether the salary of the first one rises faster than salary of the other one?
I wanted to do two separated linear regressions $Y_A=n_A+k_A \cdot X+\epsilon_A$ and $Y_B=n_B+k_B \cdot X+\epsilon_B$, where $Y_A$ and $Y_B$ represent salaries. How would I test the null hypothesis $H_0 : k_A=k_B$ against $H_1: k_A \neq k_B$? I know I could use F-test if all I wanted to test was if $k_A=0$ against $k_A \neq 0$, but don't know how to proceed in this case.