Least-squares regression earns its name because the fitting rule minimises the sum of the squared:

1. The name describes what quantity the procedure makes as small as possible. 2. Each point's vertical gap from the line is its residual. 3. The term y0 minus y-hat0 is called the error or residual. 4. The line that minimises the total of those squared errors is called a Line of Best Fit or Least-Squares Line. 5. Slopes and intercepts are outputs of that minimisation rather than the thing minimised. _Source: OpenStax Introductory Statistics 2e (CC BY 4.0), Ch 12 'Linear Regression and Correlation', sections 12.1-12.6_