6.4-03 Polynomial and basis-function fitting

Polynomial and basis-function fitting

A model may be nonlinear in its input while remaining linear in its unknown coefficients. Practice builds design rows for polynomials and fixed basis functions, checks rank, compares equivalent bases and examines transformed-response objectives.

What you will practise

• Evaluate monomial and nonmonomial design columns.
• Recognize linear versus nonlinear parameter dependence.
• Use distinct inputs to assess polynomial rank.
• Distinguish original-scale and transformed-scale fitting.

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 straight-line least squares and polynomial algebra. Keep a written calculation or short justification for each response, especially when several statements can be correct. This microlearning supports flexible linear models without losing control of the fitting objective within Module 6 of the Complete Linear Algebra Course.