Coefficients and Datasets 1

Understanding OLS coefficient stability under data duplication

This is an easy statistics question that tests your grasp of how ordinary least squares (OLS) behaves when the underlying data geometry changes. It appears frequently in quant interview screening, since the answer hinges on a foundational property of the regression estimator.

The core skill being probed is whether you understand what OLS actually minimizes: whether you can reason about the objective function and how it responds to scaling the dataset. This question rewards insight over calculation — you don't need to expand matrices or solve systems, just to think clearly about what happens to the geometry of the problem when every observation is repeated.

• The sum-of-squares objective and its invariance properties
• How sample size relates to coefficient estimates versus standard errors
• Geometric intuition for the regression line