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Scatter Plot Maker

Paste pairs of X and Y values to plot them instantly. Add a line of best fit (linear, quadratic, exponential, logarithmic or power) with its equation, see the correlation coefficient r and R², label your axes and download a crisp PNG.

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How to use the Scatter Plot Maker

  1. Paste your data: one X,Y pair per line, or copy two columns from Excel or Google Sheets. A third column can hold point labels.
  2. Choose a trendline type, or None for just the points.
  3. Read the results: equation of the line, R², the correlation coefficient r and how strong the relationship is.
  4. Label the chart with a title and axis names and adjust colors and point size.
  5. Download PNG or copy the results for your report.

Formulas used

For n points (x, y) with means x̄ and ȳ:

  • Slope: b = Σ(x − x̄)(y − ȳ) ÷ Σ(x − x̄)²
  • Intercept: a = ȳ − b·x̄, so the line of best fit is y = a + bx
  • Pearson correlation: r = Σ(x − x̄)(y − ȳ) ÷ √[Σ(x − x̄)² · Σ(y − ȳ)²]
  • Coefficient of determination: R² = 1 − SSres ÷ SStot, where SSres = Σ(y − ŷ)² and SStot = Σ(y − ȳ)²

With the sample data (hours studied vs. exam score, n = 12) the least-squares line is y ≈ 46.11 + 4.92x with r ≈ 0.987 and R² ≈ 0.973: each extra hour of study goes with roughly 5 more points, and the line explains about 97% of the variation in scores.

Which trendline should I choose?

TrendlineEquationTypical pattern
Lineary = a + bxPoints fall roughly along a straight line
Quadraticy = a + bx + cx²One bend: rises then falls (or the reverse), e.g. projectile height
Exponentialy = a·e^(bx)Growth or decay by a constant percentage, e.g. compound growth, cooling
Logarithmicy = a + b·ln(x)Rises quickly then levels off, e.g. learning curves
Powery = a·x^bScaling laws, e.g. area vs. length

A higher R² means a closer fit, but do not choose a curve only because R² is higher: pick the model that makes sense for the data and check that the points scatter randomly around the line. Predictions outside the range of your X values (extrapolation) are much less reliable.

Correlation is not causation

A strong r shows that two variables move together, not that one causes the other. Ice cream sales and sunburns are correlated because both rise in hot weather. Look for confounding variables, and remember that r only measures linear association: a perfect U-shaped relationship can have r close to 0. For the full regression output see the Linear Regression Calculator and the Correlation Coefficient Calculator.

Frequently asked questions

What is a scatter plot used for?

A scatter plot shows the relationship between two numeric variables. Each point is one observation with its X value on the horizontal axis and Y value on the vertical axis. Patterns in the cloud of points reveal positive or negative correlation, curved relationships, clusters and outliers.

How is the line of best fit calculated?

The linear trendline uses ordinary least squares: slope b = Σ(x − x̄)(y − ȳ) / Σ(x − x̄)², intercept a = ȳ − b·x̄, giving y = a + bx. It is the line that makes the sum of squared vertical distances from the points as small as possible.

What is the difference between r and R²?

r (Pearson's correlation coefficient) ranges from −1 to 1 and gives the direction and strength of a linear relationship. R² (the coefficient of determination) is the share of the variation in Y explained by the trendline, from 0 to 1. For a linear trendline R² equals r squared.

What counts as a strong correlation?

A common rule of thumb for |r|: below 0.1 negligible, 0.1–0.3 weak, 0.3–0.5 moderate, 0.5–0.7 strong and above 0.7 very strong. Context matters: in physics r = 0.9 may be poor, while in social science 0.4 can be meaningful. Correlation also does not prove causation.

How are exponential and power trendlines fitted?

Like spreadsheet programs, the tool takes logarithms and fits a straight line: ln(y) = ln(a) + bx for exponential (y = a·e^(bx)) and ln(y) = ln(a) + b·ln(x) for power (y = a·x^b). R² is reported on that transformed scale. These fits require positive Y values (and positive X for power and logarithmic).

Can I label individual points?

Yes. Add a third column with a name, for example 'Paris, 2.1, 35'. Labels are shown next to the points when you tick Show point labels, and in the tooltip when you hover a point.

Is my data uploaded?

No. The chart and all statistics are calculated in your browser. The data is saved only in your browser's local storage so it is still there when you come back.

Are all the tools on FreeToolCabin tested for quality and accuracy?

Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.

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