# Regression methods for different sizes of $n$

I thought about something interesting today.
Suppose we have a regression problem where the relationship between the response and the predictor variables is approximately linear.

Let $$n$$ be the number of observations and $$p$$ the number of predictor variables.

Which regression methods would be appropriate for each individual case where

$$n$$ is $$10$$, $$1000$$ and $$100 000$$ times respectively more than $$p$$.

How would these change if interpretability is an important factor?