AP Statistics / Regression Analysis
Lesson
Scatterplots, correlation, and the line
See the association first, then summarize it with r and a least-squares equation.
Learning goals
- Describe direction, form, and strength from a scatterplot.
- Interpret slope and intercept of a least-squares line in context.
Explanation
Two quantitative variables belong on a scatterplot. Say whether the cloud rises or falls, whether it looks linear, and how tightly it hugs a line. Correlation r is a number between −1 and 1 for linear strength. It does not care which variable you call x.
The least-squares line predicts y from x by minimizing the sum of squared residuals. Slope is a predicted change. The intercept is the predicted y when x is 0, which is only meaningful when x = 0 is in range and makes sense.
Key terms
- Correlation. A unit-free measure of the strength and direction of a linear association, written r.
- Least-squares line. The line that minimizes the sum of squared vertical residuals.
Common mistakes
- Calling a strong r proof that x causes y.
- Interpreting slope without the word predicted or without units.
Practice
Original Marlow Works items. Check the answer explanation after you try.
A reporter stands at one grocery-store exit and asks shoppers whether they support a new park tax. Why is this a poor way to estimate citywide support?
Original Marlow Works item — not a College Board question.
Take your time—this is practice, not a test.
Answer explanation
If every y-value is measured in centimeters instead of meters, what happens to r?
Answer. r stays the same because correlation does not depend on units.
Changing units stretches both axes in a matching way; linear strength is unchanged.
Related resources
External links with reuse status. Marlow Works is independent and does not copy restricted exam or textbook material.
Official / link only
AP Statistics course page
Official revised 2026–27 five-unit framework.
College Board · All rights reserved · accessed 2026-10-01
Open sourceCC BY — attribution required
Collaborative Statistics
Open statistics text for distributions, probability, and inference.
Open Textbook Library listing · CC BY · accessed 2026-10-01
Open source