Scatter plot examples: positive, negative and no correlation

What it shows

Three scatter plots of simulated data, each for 30 students, with exam score (%) on the vertical axis. In the first, exam score rises with hours studied per week; in the second, it falls with hours of paid work per week; in the third, it is unrelated to height.

Each panel is labeled with its Pearson correlation coefficient, r, computed from the plotted values. The data are illustrative, generated with a seeded random number generator, and each dot is one student.

How to read it

1. 1

   Look at the direction of the cloud first. Rising from left to right is positive correlation (r = 0.89); falling is negative correlation (r = −0.79).

2. 2

   In the third panel the points form no pattern, and r = 0.05, close to zero.

3. 3

   The closer the points sit to a straight line, the stronger the correlation and the further r is from zero.

4. 4

   Where two students share the same values, one dot is marked “×2”.

The numbers behind it

• Positive panel: hours studied per week, spread across 0 to 20; score = 42 + 2 × hours + normal noise (SD 7); r = 0.89.
• Negative panel: hours of paid work per week, spread across 0 to 20; score = 85 − 1.5 × hours + normal noise (SD 7); r = −0.79.
• No-correlation panel: height normal with mean 170 cm and SD 9 cm; score drawn independently of it (mean 68, SD 10); r = 0.05.
• Values are rounded to whole hours, centimeters and percent before r is computed; 30 students per panel.

Ways to use it in teaching

• Cover the r values and have students rank the three panels by strength of relationship before revealing them.

• r near zero rules out only a straight-line relationship; a curved one can also give r near zero, unlike the height panel, where there is no relationship at all.

• Ask which of the two correlated pairs could plausibly be causal, and what a study would need to show it.

Correlation is the first step toward the tests in our guide to inferential statistics.

Sources

• Çetinkaya-Rundel, M., & Hardin, J. (2024). Introduction to modern statistics (2nd ed.). OpenIntro. https://openintro-ims.netlify.app/
• Pearson correlation coefficient. (n.d.). In Wikipedia. Retrieved October 18, 2026, from https://en.wikipedia.org/wiki/Pearson_correlation_coefficient
• Scatter plot. (n.d.). In Wikipedia. Retrieved October 18, 2026, from https://en.wikipedia.org/wiki/Scatter_plot