Two-Variable Data • Topic 4 of 5

Negative Correlation

A negative correlation means that as one variable increases the other tends to decrease, so the line of best fit slopes downward (negative slope). Common examples are a car’s age and its resale value, altitude and air temperature, or absences from class and final grade. As with positive correlation, the strength varies with how tightly the points cluster, but the direction is always downward. The SAT tests this by asking which pair of variables shows a negative correlation, or by having you recognise a downward trend on a scatterplot or a negative slope in a line of best fit.

Ten points falling left to right with a falling line of best fitNegative correlationxyOne increases as the other decreases.

✅ Solved examples

1. A car’s age and its resale value — what correlation?
Older cars are worth less: negative.
2. A line of best fit has slope −3. What correlation?
A negative slope shows a negative correlation.
3. Altitude and air temperature — correlation?
Higher altitude, lower temperature: negative.
4. Class absences and final grade — correlation?
More absences, lower grade: negative.

✏️ Practice — try these, take hints as needed

1. Outdoor temperature and heating costs — what correlation?
As temperature rises, heating cost…
Falls.
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Negative.
2. Practice time and number of mistakes — correlation?
More practice, fewer mistakes.
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Negative.
3. A line of best fit slopes downward. Correlation?
Downward slope.
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Negative.
4. A phone battery’s age and its capacity — correlation?
Older battery, less capacity.
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Negative.
5. Speed of travel and time taken for a fixed distance — correlation?
Faster means less time.
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Negative.

📝 Topic test — 8 questions

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