$$y_i = \beta_{0} + \beta_{1}x_{1i} + \varepsilon_{0i}$$
The language to describe regression models, such as the very simple linear regression specified above often varies and such variations often carry subtle shifts in meanings. For example, the part of the model on the left-hand side of the equation may be termed (among others I am ignorant of) with connotations and denotations in parentheses:
- Dependent variable (hints at causal dependence)
- Predicted variable (implies the model forecasts/makes predictions)
- Response variable (implies causality, or at least temporal sequencing)
- Outcome variable (implies causality)
The variation in nomenclature is also true on the right-hand side of the equation (same disclaimer that I am an ignoramus about other terms):
- Independent variable (implies causal priority, hints at experimental design)
- Predictor variable (implies forecasts, implies that the variable has a non-zero parameter estimate associated with it)
In the course of proposing vetting, or communicating research I have had occasion to not only be called on the use of one term or another, but to subsequently be called on the term I chose to replace it with. While the people calling were of course being pedantic (NB: I am a professional pedant, so I sympathize), because of course we all understood what was being communicated, I still wonder:
Are there commonly used terms for the left-hand and right hand variables in regression models that are agnostic with respect to (a) the external uses of the model, (b) causal relationships between the variables, and (c) aspects of the study designs used to produce the variables themselves?
NB: I am not asking about the important issues of proper modeling and proper interpretation (i.e. I care very much about causality, study design, etc.), but am more interested in a language for talking about such models generally.
(I realize that "left-hand variables" and "right-hand variables" might, I suppose, be construed as a credible answer, but these terms seem clunky... maybe this is a clunky question. :)