Scatter Plot Maker
Scatter Plot Examples
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What Is a Scatter Plot?
A scatter plot (scatter graph or scatter diagram) displays the relationship between two quantitative variables by plotting one variable on the x-axis and another on the y-axis. Each observation becomes a point on the graph. The overall pattern of points reveals whether the variables are correlated — and if so, how strongly and in which direction.
Scatter plots are the first and most important tool for exploring bivariate data. Before calculating any correlation coefficient or fitting a regression line, always look at the scatter plot — it reveals non-linear patterns, outliers, clusters, and heteroscedasticity that summary statistics would miss.
Pearson Correlation Coefficient (r)
| r value | Interpretation | Example relationships |
|---|---|---|
| +0.9 to +1.0 | Very strong positive | Height vs wingspan, temperature vs ice cream sales |
| +0.7 to +0.9 | Strong positive | Hours studied vs exam score, income vs spending |
| +0.4 to +0.7 | Moderate positive | Exercise vs fitness level, education vs salary |
| −0.4 to +0.4 | Weak or no linear correlation | Shoe size vs IQ, birth month vs achievement |
| −0.7 to −0.4 | Moderate negative | TV hours vs grades, stress vs sleep quality |
| −1.0 to −0.7 | Strong negative | Speed vs travel time, altitude vs temperature |
Correlation vs Causation
A high correlation coefficient does not imply causation. Two variables can be strongly correlated because they share a common cause (confounding variable), because of coincidence in the sample, or because of reverse causation. Always consider alternative explanations before concluding that X causes Y. The classic example: ice cream sales and drowning deaths are both higher in summer — they are correlated but neither causes the other; both are caused by warm weather.
Related Topics
Sources & further reading:
- NIST Engineering Statistics Handbook — Scatter Plots
- Anscombe, F.J. (1973). Graphs in Statistical Analysis. The American Statistician, 27(1), 17–21. [Anscombe's quartet demonstrates importance of visualization]
Frequently Asked Questions
A scatter plot shows the relationship between two quantitative variables. Each point represents one observation (case). The overall pattern reveals: direction (positive or negative), strength (tight cluster vs scattered cloud), form (linear vs curved), and outliers. It's the essential first step before calculating correlation or fitting a regression line.
R² (the coefficient of determination) measures how much of the variation in Y is explained by the linear relationship with X. R² = r². An R² of 0.75 means 75% of the variability in Y is explained by the regression line. The remaining 25% is unexplained variance (residuals). R² ranges from 0 (no linear fit) to 1 (perfect fit).
Select "Show regression line" in the options. The regression line (line of best fit) minimizes the sum of squared residuals. The equation ŷ = b₀ + b₁x appears on the chart, where b₀ is the y-intercept and b₁ is the slope. The slope tells you: for every 1-unit increase in X, Y changes by b₁ units on average.
No. Correlation measures the strength and direction of a linear relationship, but does not establish causation. Two variables can be correlated because of a confounding variable (a hidden common cause), coincidence in the sample, or reverse causation. To establish causation, you need a properly designed randomized controlled experiment, not just observational data.