I'm surprised I haven't run into this question yet, but I was wondering if there is a sound way of testing the difference in predicted means between two points on the same slope.
For example: Let's say my predictor is the age of a car, and my predicted variable, its price. Let's assume that the downward slope is significant. What I would like to test is if a car 5 years old is significantly cheaper than one that is a year old.
Can I just use the two predicted means, and divide them by some error term as a t-test? And if so, which error term?