6.4-02 A best-fit straight line

A best-fit straight line

Build and solve best-fit straight-line models from small data sets. The questions connect intercept and slope calculations with centered inputs, residual conditions, prediction, rank deficiency and the distinction between vertical and perpendicular error.

What you will practise

• Construct a line-design matrix.
• Solve for intercept and slope.
• Check fitted predictions and residual constraints.
• Handle repeated inputs and through-origin models.

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 normal equations and basic algebra. Keep a written calculation or short justification for each response, especially when several statements can be correct. This microlearning supports polynomial and multi-feature regression within Module 6 of the Complete Linear Algebra Course.