Scatter Plot & Correlation

Upload a CSV file or paste tabular data, choose two numeric columns, and instantly see how they relate. This tool draws a scatter plot in your browser, computes the Pearson correlation coefficient, and optionally overlays a linear regression line — all without sending any data to a server.

What is a scatter plot?

A scatter plot (also called a scatter graph or XY plot) places paired observations as dots on a two-dimensional plane. Each dot has an X coordinate from one variable and a Y coordinate from another. The resulting cloud of points reveals the shape, strength, and direction of the relationship between the two variables.

Looking at a scatter plot you can quickly answer:

• Is there a positive relationship (as X increases, Y tends to increase)?
• Is there a negative relationship (as X increases, Y tends to decrease)?
• Is the relationship linear (dots cluster around a straight line) or curved?
• Are there outliers — points far from the main cluster?
• Are there subgroups — multiple distinct clouds that suggest hidden categories in the data?

Scatter plots are foundational to exploratory data analysis (EDA). Before applying any statistical test or machine learning model, visualizing your data as a scatter plot can save hours of wasted effort by revealing structure that summary statistics alone miss.

Pearson correlation coefficient (r)

The Pearson r is the most common single-number summary of a linear relationship. It ranges from -1 to +1:

• r = +1: perfect positive linear relationship — all points lie exactly on an upward-sloping line.
• r = 0: no linear relationship — knowing X gives no information about Y under a linear model.
• r = -1: perfect negative linear relationship — all points lie exactly on a downward-sloping line.

Conventional strength guidelines (Cohen, 1988): |r| < 0.1 is negligible; 0.1–0.3 small; 0.3–0.5 moderate; 0.5–0.7 large; > 0.7 very large. These thresholds vary by discipline — in physics an r of 0.9 might be unimpressive, while in social science it would be remarkable.

Important caveats:

1. r measures only linear association. Two variables can be strongly related in a curved (nonlinear) way yet have r close to zero. Always look at the plot.
2. Correlation does not imply causation. A high r between ice cream sales and drowning rates does not mean ice cream causes drowning — both are driven by hot weather.
3. Outliers can inflate or deflate r dramatically. One extreme point can shift r by 0.3 or more.
4. Anscombe’s Quartet (1973) famously showed four datasets with identical r ≈ 0.816 but wildly different scatter plots. Always visualize your data.

R² — coefficient of determination

R² is simply r², and it has a more intuitive interpretation: it is the proportion of variance in Y that is linearly explained by X. For example, if r = 0.8, then R² = 0.64, meaning 64% of the variation in Y is accounted for by the linear relationship with X. The remaining 36% is due to other factors, measurement error, or nonlinearity.

R² is also reported by this tool alongside r so you can see both the direction (sign of r) and the explanatory power (R²) at a glance.

Linear regression

When you check Show regression line, the tool computes a simple ordinary least squares (OLS) regression: it finds the straight line ŷ = slope · x + intercept that minimises the sum of squared vertical distances (residuals) from each point to the line.

• Slope: how many units Y changes on average for each one-unit increase in X.
• Intercept: the predicted value of Y when X = 0 (may not be meaningful if X = 0 is outside your data range).

The regression line passes through the point (x̄, ȳ) — the joint mean of both variables. The slope equals Cov(X, Y) / Var(X). The R² of the regression line equals r².

When is regression useful?

• Prediction: given a new X value, use the line to estimate Y (within the range of your data — extrapolation is risky).
• Effect size: the slope tells you the practical magnitude of the relationship, not just its direction.
• Communication: a trend line on a scatter plot makes the relationship concrete and easy to explain to non-statisticians.

How to use this tool

1. Upload your data: drag and drop a CSV file, click “Choose file”, or paste comma- or tab-separated text into the textarea. The tool auto-detects delimiters and column headers.
2. Select X and Y columns: any two numeric columns. You can swap them to flip which variable is treated as independent.
3. Read the stats: Pearson r and R² are shown immediately below the chart.
4. Toggle the regression line: check “Show regression line” to overlay the OLS fit with slope and intercept displayed.
5. Explore: try different column pairs to understand the structure of your dataset.

Common use cases

• Biology / medicine: height vs weight, dose vs response, age vs blood pressure.
• Finance: price vs volume, returns vs market index (beta estimation).
• Education: study hours vs exam score, class size vs performance.
• Engineering: input voltage vs output current, temperature vs resistance.
• Marketing: ad spend vs sales, customer reviews vs churn rate.

Privacy

All computation happens locally in your browser using JavaScript. No data is transmitted to any server. The maximum recommended file size is 5 MB; very large files (> 100,000 rows) may be slow to render.

References

• Pearson, K. (1895). Notes on regression and inheritance in the case of two parents. Proceedings of the Royal Society of London.
• Galton, F. (1886). Regression towards mediocrity in hereditary stature. Journal of the Anthropological Institute, 15, 246–263.
• Anscombe, F. J. (1973). Graphs in statistical analysis. The American Statistician, 27(1), 17–21.
• Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Erlbaum.