Changes-leading-to-changes

A quick illustration of how talking about changes in a variable X leading to changes in another variable Y can be simplified.

Changes-leading-to-changes makes language difficult, because we are used to talk about ‘imaginary changes in X leading to imaginary changes in Y’ to describe Y(X) relations from cross-sectional/timeless regressions X->Y, whereas in reality there are no actual changes to talk about in the same-time Y-on-X regression, only potential ones.

The problem comes when talking about what a model 'change-in-X->change-in-Y' tells us; here, you run into the problem of having cases that belong to 4 different quadrants of a scatter plot change-in-Y(change-in-X), see figure above: those increasing in both (Q2), those decreasing in both (Q4), and those increasing in 1: Y/X and decreasing in the other one: X/Y (Q1 / Q3, respectively).
You can still talk about all of these, with some help from peeking at where the averages for change-in-X & change-in-Y are (see the big green dot), whether they are positive or negative.

A simple way of describing these graphs where the changesX->changesY slope is >0 , is to say that if one increases in X, then we expect their Y to also increase, even though the 2 graphs show that the Y actual mean shows an average Y increase, then an average Y decrease: the only difference is that the slope was 'pushed down' by the 2 means, as the slope naturally crosses the (MeanX, MeanY) dot.