Regression summary

Key learning points

• The regression line of $y$ on $x$ minimises vertical residuals.
• Interpret the gradient as change in $y$ per unit $x$.
• Prefer interpolation; avoid reckless extrapolation.
• Judge fit with residuals and the scatter diagram.

Worked example 1 — Extrapolation

Why avoid predicting far outside the data range?

Working

Extrapolation is unreliable.

Worked example 2 — The regression line of on minimises vertical residuals

Use this method from the Regression sheet: The regression line of $y$ on $x$ minimises vertical residuals.

Working

Each key learning point matches a question type on the printable worksheet.

Worked example 3 — Interpret the gradient as change in per unit

Use this method from the Regression sheet: Interpret the gradient as change in $y$ per unit $x$.

Working

Each key learning point matches a question type on the printable worksheet.

Worked example 4 — Prefer interpolation; avoid reckless extrapolation

Use this method from the Regression sheet: Prefer interpolation; avoid reckless extrapolation.

Working

Each key learning point matches a question type on the printable worksheet.

Worked example 5 — Judge fit with residuals and the scatter diagram

Use this method from the Regression sheet: Judge fit with residuals and the scatter diagram.

Working

Each key learning point matches a question type on the printable worksheet.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.