Given a data set of 100n=100 observations, (n=100) withk=50 independent variables xi, and one dependent variable (y) and 50 independent variables (k=50). Inference, inference answers the following two questions such as:
- WhichWhat subset of or combination of the 50k independent variables affect y?
- If I were able to increase the value of x1 by 10%, how much would y increase? (i.e. ∂y∂x1)
Both of these questions are questions about the parameters in the “true model” that generated the data.
Prediction answers a much simpler question:
- Given new values for eachIf we set the independent variablevariables xi to some specific values, what'swhat is my best guess offor y?
The lastThis question does not ask anything about the parameters in the true model. Nor does it necessarily appeal torequire the existence of a “true model”. SimplyPrediction simply involves a plug-and-chug that generatesto generate a value ^yiˆy that is ideally close to yiy.