I hope someone can help and that this is not a simple repeat of other questions on here - none seem to quite match what I'm looking for. (Or, I have become confused by terminology...)
THE PROBLEM I have conducted OLS regression for the yearly mean values of a measured variable vs time (year), from 13 different locations. So, I have 13 different regression equations, where the independent variable, year, is the same for each, but the dependent variable (mean of the measured variable) differs. The slope of some of the lines varies qualitatively, but I want to be able to support/reject this with a statistical test. I am ultimately trying to demonstrate that the rate of change over time of my measured variable depends on location (which can be explained by physical reasons). What test can/should I do?
I have looked into ANCOVA, but I'm not sure that this is what I want, as (unless I am confused) this seems to be a test for equality of y-intercept assuming the slopes of the lines are equal?