Correlation and Regression Topic Review summary

Key learning points

• PMCC $r$ measures linear strength/direction; $-1\\le r\\le 1$.
• Regression line $y=a+bx$ minimises vertical least squares; $b=\\frac{S_{xy}}{S_{xx}}$.
• Interpret gradient and intercept in context; interpolation vs extrapolation.
• Coding affects calculations — know the effect on $r$ (invariant to linear coding).
• Correlation ≠ causation — comment when asked.

Worked example 1 — r

What does $r\\approx 0$ suggest?

Working

Nonlinear links may still exist.

Worked example 2 — Predict

Use $y=a+bx$ inside the data range.

Working

State the caveat in exams.

Worked example 3 — PMCC r measures linear strength/direction;

PMCC $r$ measures linear strength/direction; $-1\\\\le r\\\\le 1$.

Working

Attempt without notes, then check the answers PDF.

Worked example 4 — Regression line y=a+bx minimises vertical

Regression line $y=a+bx$ minimises vertical least squares; $b=\\\\frac{S_{xy}}{S_{xx}}$.

Working

Attempt without notes, then check the answers PDF.

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.