Correlation Is Not Necessarily Causation

We’ve been cautious when interpreting regression slope coefficients. We always discuss the associated effect of an explanatory variable $x$ on an outcome variable $y$. For example, for our statement, “For every increase of 1 unit in bty_avg, there is an associated increase of on average 0.067 units of score,” we include the term “associated” to be extra careful, not to suggest we’re making a causal statement. Even though the beauty score of bty_avg is positively correlated with the teaching score, we can’t necessarily make any statements about beauty scores’ direct causal effect on teaching scores. We need more information on how this study was conducted.