Two-Variable Data • Topic 3 of 5

Positive Correlation

A positive correlation means the two variables tend to increase together: as one goes up, so does the other, so the line of best fit slopes upward (positive slope). Everyday examples include height and shoe size, hours worked and total pay, or study time and exam score. The strength can still vary — a positive correlation can be strong or weak depending on how closely the points follow the line — but the direction is always upward. On the SAT you may be asked which pair of variables shows a positive correlation, or to recognise an upward trend on a scatterplot or from a positive slope.

Ten points rising left to right with a rising line of best fitPositive correlationxyBoth variables increase together.

✅ Solved examples

1. Hours worked and total pay — what correlation?
More hours means more pay: positive.
2. A line of best fit has slope +4. What correlation does that show?
A positive slope shows a positive correlation.
3. Study time and exam score tend to rise together. Correlation?
Both increasing: positive.
4. House size and price both increase. Correlation?
Positive.

✏️ Practice — try these, take hints as needed

1. A person’s height and shoe size — what correlation?
Do both rise together?
Yes.
—
Positive.
2. Distance run and calories burned — correlation?
Both increase together.
—
—
Positive.
3. A line of best fit slopes upward. What correlation?
Upward slope.
—
—
Positive.
4. Rainfall and crop yield rise together. Correlation?
Both up.
—
—
Positive.
5. Years of education and average income — correlation?
Both tend to rise.
—
—
Positive.

📝 Topic test — 8 questions

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