6.4-05 Weighted least squares

Weighted least squares

Weighted least squares changes the relative cost of observation errors. Through explicit calculations and structural questions, this set explains positive weights, square-root row scaling and the geometry underlying weighted normal equations.

What you will practise

• Form and solve weighted fitting problems.
• Convert positive weights to a scaled ordinary problem.
• Check weighted residual conditions.
• Investigate common rescaling, zero weights and invalid negative weights.

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 ordinary least squares and diagonal matrices. Keep a written calculation or short justification for each response, especially when several statements can be correct. This microlearning supports modeling unequal observation priorities with clear mathematical assumptions within Module 6 of the Complete Linear Algebra Course.