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**mathbeginner97** Thanks so much! Now it makes a lot more sense, if I'm understanding it right that is. So basically when you have a lin-log model, and you look at the change in Y, you look at the relative change in x because that's the derivative of a log or ln function. deltay / deltax is approximately equal to the derivative of y with respect to x when the change is tiny. I read about first principles, and that's how they introduce how the derivative comes about so it makes sense when I think of why the two are approximately equal. Then when you do the thing you did in your first post, you find that Beta1*ln(x) is approximately the change in y when x is small. When you multiply Beta1 by that tiny number you roughly get the change in y. Is that right?

By the way, interpreting the coefficient B1 lin-log models is only relevant when x changes by a tiny amount like 0.01 or 0.03 right? Based on what I know and what I understand from this thread, if the relative change in x is like 2.5 (as opposed to 0.01), it doesn't work.

By the way, why did you say we don't need to be exact with logs in your last post?