I faced an interview question for a job where interviewer asked me suppose your $R^2$ is very low (between 5 to 10%) for a price elasticity model. How would you solve this question?
I couldn't think of anything else other than the fact that i will do regression diagnostics to see what went wrong or if any non linear method should be applied. Somehow i think interviewer was not satisfied with my answer. Is there something else that is done in such a scenario to fit a model and use it for production level prediction despite it having low $R^2$?
Edit: At a later stage they gave me the data to model the problem during interview and i tried adding lagged variables, impact of competitor price, seasonality dummies to see if it made any difference. $R^2$ went to 17.6 percent and its performance on holdout sample was poor. Personally i think its unethical to put such a model for prediction in live environment as it will give erroneous results and result in clients loss(imagine using pricing recommendation from such a model on your company revenue!). Is there anything else that is done in such scenarios which is too obvious that everyone needs to know? Something that i am not aware of, which i am tempted to say 'a silver bullet'?
Also, lets imagine after adding exogenous variable $R^2$ improves by further 2% then what can be done in this scenario? Should we discard the modelling project or there is still some hope of developing a model of production level quality which is indicated by performance on holdout sample?