Scatter Plot Maker

A scatter plot is a graph that shows the relationship between two numeric variables, with one point for each pair of values. It is also called a scatter graph, scatter diagram, scattergram or XY chart. Each observation is one point: its x value sets how far along the horizontal axis it sits, and its y value how high it sits. The x axis usually holds the explanatory variable (the one you change or that comes first) and the y axis the response.

The pattern of the points shows whether the two variables are related: the direction (do they rise together or move in opposite directions), the strength (how tightly the points follow a line), the form (straight or curved) and any outliers. A line of best fit, also called a trend line or regression line, summarizes a straight-line pattern with an equation, y = mx + b, that you can use to describe the relationship and make predictions.

Describe a scatter plot by four things:

• Direction. Points rising from left to right show a positive correlation (taller people tend to weigh more); points falling show a negative correlation (heavier cars tend to get fewer miles per gallon). A shapeless cloud means no correlation.
• Strength. The tighter the points hug a line, the stronger the relationship. The correlation coefficient r puts a number on it: r = 1 is a perfect rising line, r = −1 a perfect falling line, and r near 0 means no straight-line relationship.
• Form. If the points bend, a straight line is the wrong summary, and r can be small even when the two variables are clearly related.
• Outliers and clusters. A single point far from the rest can pull the line toward it, as in the Anscombe example above.

Two cautions apply to every scatter plot. Correlation is not causation: ice cream sales and sunburn rise together because both follow the weather. And look before you trust r: Anscombe's four datasets share the same r, 0.816, and the same line, yet look completely different when plotted. If you have one measurement per subject in several groups rather than two measurements per subject, compare the groups with a box plot instead.

r, the Pearson correlation coefficient, runs from −1 to 1. Its sign gives the direction of the relationship and its size the strength. R², the coefficient of determination, runs from 0 to 1 and is the share of the variation in y that the line accounts for. For a straight line fitted to one x variable, R² is simply r squared: r = 0.9 gives R² = 0.81.

Report r when the question is how strongly two variables are related, and R² when the question is how well the line predicts y. R² loses the sign, so with R² alone readers cannot tell a rising line from a falling one; the equation's slope tells them. This tool shows both, along with a correlation word (weak, moderate, strong) based on a common rule of thumb.

Paste numbers in any of these layouts:

Tabs (what spreadsheets copy), commas, semicolons and spaces all work. Rows with a missing x or y are left out, and cells such as NA are skipped and counted under the box. The first column of numbers is always used as x.

• Excel: select the two columns, then Insert › Insert Scatter (X, Y) › Scatter. For the line, right-click a point › Add Trendline › Linear, and tick Display Equation on chart and Display R-squared value on chart.
• Google Sheets: select the columns, Insert › Chart, set Chart type to Scatter chart, then in Customize › Series tick Trendline and set Label to Use Equation and tick Show R².
• Desmos: type the pairs into a table, then in a new line type y1 ~ mx1 + b to get m, b, r and R².
• TI-84: enter x in L1 and y in L2, turn on STAT PLOT with the scatter type, then STAT › CALC › LinReg(ax+b). Turn on DiagnosticOn to see r and r².
• R: ggplot(df, aes(x, y)) + geom_point() + geom_smooth(method = "lm"), with summary(lm(y ~ x, data = df)) for the numbers.
• Python: plt.scatter(x, y) in matplotlib, with numpy.polyfit(x, y, 1) or scipy.stats.linregress(x, y) for the line.

All of these fit the line by least squares, so on the same data they give the same slope, intercept, r and R² as this tool, up to rounding. Use this page when you need the figure now, want the working shown, or want labeled points and several groups without building the chart by hand.

This tool fits straight lines only. If your points bend (growth that speeds up, a curve that levels off, a U shape), a straight line will miss the pattern and r will understate how related the variables are. For a curve of best fit, use Desmos (y1 ~ a·x1² + b·x1 + c or y1 ~ a·b^x1), Excel's Exponential, Logarithmic, Polynomial or Power trendlines, or geom_smooth() in R. A scatter plot from this tool, with the line turned off, is still a good way to see the shape first.

Whoever reads your figure, a teacher, a lab supervisor or a reviewer, will look for the same things:

1. Axis labels with units: Weight (1,000 lb), not Weight.
2. n, the number of points, in the caption or the text.
3. The line's equation and r or R², if you drew a line, with the slope interpreted in words.
4. Which variable is x, and why: the explanatory variable goes on x.
5. A test of significance if your course asks for a p-value. This tool reports the equation, r and R² only, so get the p-value from Excel's Data Analysis › Regression, a TI-84 LinRegTTest, R or SPSS.

A caption you can adapt: “Scatter plot of test score against hours studied for 10 students. The line is the least-squares fit, y = 4.968x + 47.04 (R² = 0.967).”