I was given a question as part of the interview process for a job and I was looking for some advice. In this question I was given some (x,y) data (both univariate) and was asked to construct a mathematical model. Literally no other information was given. So I'm wondering what to do here. I could fit the data with a polynomial model such that the error is zero, however this would obviously overfit the data hugely. However, the question never mentions anything about using the model for prediction. So should I try to reduce overfitting or not? I'm wondering if anyone could give me some advice for this.
I agree, you could do that, but that is definitely overfitting the model. In addition, this is difficult as you do not have any information for what the model will be used for. Personally, I would present both a simple linear regression (after performing the appropriate regression diagnostics) as well as the polynomial function of degree 99.
Additionally, it may be helpful to provide the pros and cons of each regression model in regards to your data/overfitting.
It shows that you thoroughly thought about the task at hand and are able to come up with more than one solution to a given problem. Both must haves for a new hire! Best of luck!