Models and relationships
Regression and the diagnostics around it: what a coefficient claims, what R-squared does not, and the two ways a good-looking model misleads you.
Regression is the tool underneath most of the measurement on this site — marketing mix models, variance reduction, matched-market analysis — and the terms here are what it means and how it fails. The failures are worth as much attention as the method, because a model that is wrong in these specific ways still produces confident numbers and a respectable fit statistic.
The first is reading a coefficient as an effect. Regression analysis estimates an association holding the other included variables fixed, and that is a causal claim only if the right variables were included and nothing was left out. The second is trusting fit: R-squared says how much variance the model explains in the data it was fitted on, which is a different thing from whether it will be right about anything new.
Two specific pathologies get their own entries because both are common and neither is visible in the summary output. Multicollinearity — correlated inputs — leaves the model's predictions fine and its individual coefficients unstable, which is fatal precisely when you wanted to read one of them as a channel's contribution. Overfitting is a model that has learned the noise, and it looks best exactly when it is worst.