6.4-07 Checking fit quality

Checking fit quality

Assess a fit by examining its residuals and the meaning of its error measure. The questions combine error calculations with structured residuals, held-out checks, scale effects and the limitations of numerical optimality alone.

What you will practise

• Calculate squared error and a stated RMSE.
• Interpret patterns in residuals.
• Distinguish training fit from generalization.
• Understand what normal-equation checks establish.

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 least-squares residuals and basic squared-error arithmetic. Keep a written calculation or short justification for each response, especially when several statements can be correct. This microlearning supports responsible evaluation of fitted models within Module 6 of the Complete Linear Algebra Course.