Linear Regression Basics

Understanding why linear regression uses squared errors

This foundational statistics question tests whether you grasp the reasoning behind the ordinary least squares (OLS) criterion — one of the most widely used optimization objectives in quantitative finance and data science. It surfaces a common misconception among candidates new to regression.

The question probes your intuition about loss functions: specifically, why squaring errors matters more than simply summing raw deviations. A solid answer demonstrates understanding of how squaring penalizes large misses, ensures a unique mathematical solution, and produces interpretable statistical properties. Quant researchers and trading-desk analysts use regression constantly, so firms expect candidates to know not just how to fit a line, but why the standard formulation works.

• Loss functions and their mathematical properties
• Sensitivity to outliers in fitted models
• Optimization and the role of convexity
• Comparison of L1 vs. L2 error metrics