Suppose we take the classical linear regression model:
$$y_i = \beta_0 + \beta_1 x_i + \epsilon_i$$
Over the years, I have heard so many people say that such an interpretation can be drawn from this model:
- On average, a one unit increase in $x_i$ "causes" a $\beta_1$ unit increase in $y_i$
However, we are also told that this model can not directly imply this type of "causation". As a matter of fact, there is a whole field of Statistics that studies causality called "Causal Inference" (https://en.wikipedia.org/wiki/Causal_inference).
In general, is there any language that can be used to interpret this kind of model without suggesting any misleading claims about causality?