6.4-01 Least squares as a closest-point problem

Least squares as a closest-point problem

Least squares finds the reachable output closest to a target when exact equations may be inconsistent. This set emphasizes observation-space geometry, the meaning of the objective, and what changes when the available model space grows.

What you will practise

• Interpret squared residual objectives.
• Compute a simple constant fit.
• Explain existence and closest-point uniqueness.
• Separate fitting error from coefficient size and prediction quality.

Begin with recognition and interpretation, then work through calculations, error diagnosis and more demanding reasoning. Single-select and multi-select questions ask you to evaluate the stated assumptions as well as the result. Worked explanations connect the answer to a method or a counterexample, so you can check why tempting alternatives fail.

Before you start

Review column spaces and orthogonal projection. Keep a written calculation or short justification for each response, especially when several statements can be correct. This microlearning supports building and comparing linear data-fitting models within Module 6 of the Complete Linear Algebra Course.