Scatter Plot Maker

Paste paired values — X on the left, Y on the right, one observation per position — and the plot draws in your browser. Commas, spaces, newlines and pasted spreadsheet columns all work, the trendline checkbox fits a least-squares line, and the camera icon exports a PNG.

What a Scatter Plot Is For

Every other chart on this site summarises one variable. A scatter plot is the tool for the question "do these two things move together?" — two continuous measurements taken on the same set of subjects, plotted as one point per subject. Height against weight for 200 people. Advertising spend against sales for 40 weeks. Engine size against fuel consumption for 60 cars.

The requirement is pairing. Position 7 in the X box and position 7 in the Y box must be two measurements of the same store, the same week, the same patient. If you sort one column in a spreadsheet without sorting the other, every pair is destroyed and the chart is meaningless while still looking perfectly plausible. Sort both together, or paste the whole table into each box and pick the column you want.

Reading the Cloud: Direction, Form, Strength, Outliers

Four things are worth naming out loud every time you look at one, in this order:

Direction. Does the cloud slope up (as X rises so does Y, a positive relationship), down (negative), or neither?

Form. Is it a straight band, a curve, a fan that widens to the right, or two separate clumps? Form comes before strength, because a strong curved relationship and a weak straight one can produce the same correlation number. Two distinct clumps usually mean you have two populations mixed together and should be plotting them separately.

Strength. How tightly do the points hug the underlying shape? A narrow band means X predicts Y well; a wide cloud means it barely helps. The correlation coefficient r runs from −1 to +1, and squaring it gives the share of variation in Y that moves with X — r = 0.7 means about 49%. What counts as "strong" is field-dependent: 0.5 is a large effect in psychology and a poor calibration in a physics lab.

Outliers. Points far from everything else. Look at each one before doing anything: a genuine extreme observation tells you something, a typo tells you nothing, and both drag a fitted line toward themselves.

Correlation Is Not Causation, Concretely

The slogan is repeated so often it stops registering, so here is what it costs. Ice cream sales correlate strongly with drowning deaths. Neither causes the other; hot weather causes both, by driving people to buy ice cream and to swim. That third variable is a confounder, and no amount of extra data on ice cream and drownings will reveal it — you have to think of it and measure it.

A published example makes the same point at scale. A 2012 paper in the New England Journal of Medicine plotted national chocolate consumption per head against Nobel laureates per head across 23 countries and found a correlation of about 0.79 — stronger than plenty of relationships people act on. The plausible confounder is national wealth, which raises both chocolate spending and research funding.

Three other explanations produce the same picture:

• Reverse causation. More firefighters attend more damaging fires. The firefighters are not causing the damage.
• Selection. If your sample only contains customers who stayed, a relationship measured across them may be absent in everyone else.
• Coincidence. Test enough variable pairs and some will correlate at 0.9 with nothing behind it.

The only reliable route to causation is intervening — changing X yourself and seeing whether Y follows. A scatter plot is where a hypothesis starts, not where it is confirmed.

What the Trendline Does and Doesn't Tell You

The Show trendline checkbox fits an ordinary least-squares straight line: the line minimising the total squared vertical distance from the points. It is drawn between your smallest and largest X only, so the tool never extrapolates past your data — a deliberate limit, since a line fitted over footfall of 1,000 to 6,000 says nothing about footfall of 20,000.

Three ways it can mislead:

It is straight whether or not your data is. Fit a line to a dome-shaped relationship — yield against fertiliser, performance against arousal, anything with an optimum — and you get a nearly flat line and a correlation near zero, implying no relationship where a strong one exists. Look at the cloud first; if it curves, the line is the wrong summary and the slope is not a rate of anything.

A few points can own it. Least squares squares the residuals, so a point twice as far from the line has four times the pull. One mistyped value at the edge of the X range can set the slope on its own.

The intercept is usually extrapolation. Where the line meets X = 0 is generally outside your data and should not be read as a prediction.

Anscombe's Quartet

In 1973 the statistician Francis Anscombe published four datasets of eleven points each. All four share, to two decimal places, the same mean of X (9.00), mean of Y (7.50), variance of X (11.00), variance of Y (4.12), correlation (0.816) and least-squares line (ŷ = 3.00 + 0.50x). Any summary table would call them the same data.

They look nothing alike. Set I is an ordinary noisy linear cloud. Set II is a clean curve, arching up and back down. Set III is a perfect straight line with one point thrown far off it. Set IV has ten points stacked in a single vertical column plus one distant point that produces the entire slope by itself.

Paste the shared X values with Set I's Y values, tick the trendline, then swap in Set II and generate again — the line will not move:

X  (I–III): 10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5
Y  (I):     8.04, 6.95, 7.58, 8.81, 8.33, 9.96, 7.24, 4.26, 10.84, 4.82, 5.68
Y  (II):    9.14, 8.14, 8.74, 8.77, 9.26, 8.10, 6.13, 3.10, 9.13, 7.26, 4.74

The modern sequel is the Datasaurus Dozen, published by Justin Matejka and George Fitzmaurice in 2017: thirteen datasets with matching summary statistics to two decimals, one of which draws a dinosaur. The lesson is the same either way — summary statistics describe a shape they cannot show you, and plotting costs nothing.

Overplotting on Dense Data

Below a few hundred points, a scatter plot is honest about density. Above that, markers stack on markers, and a region containing 500 observations is drawn identically to one containing 50. The chart looks confident and tells you nothing about where the mass is.

The controls on this page handle most cases. Drop Opacity to 0.2 and each point contributes a faint wash, so overlapping regions darken in proportion to how crowded they are. Drop Size to 3 or 4 so the markers stop merging. The two together turn a solid blob back into a readable density map.

Two situations need work upstream. Rounded or scale data — survey answers of 1 to 5, ages in whole years — puts every observation on a lattice of identical coordinates, and no opacity setting separates points sitting at exactly the same spot; add a small random jitter (say ±0.15) to each value in your spreadsheet before pasting. And past roughly 50,000 points, either take a random sample of a few thousand, which preserves the shape, or move to a binned view such as a hexbin or 2D histogram where colour encodes the count per cell.

Footfall Against Sales Across Fourteen Branches

Fourteen branches of a shop: X is weekly footfall in thousands, Y is weekly sales in £000.

X: 1.2, 1.8, 2.1, 2.4, 2.6, 3.0, 3.3, 3.5, 3.9, 4.2, 4.6, 5.0, 5.4, 6.1
Y: 4.1, 5.9, 5.2, 7.4, 6.3, 8.8, 7.1, 9.6, 8.4, 11.2, 9.5, 12.4, 10.8, 13.9

The cloud rises in a clear straight band. The fitted line is ŷ = 2.14 + 1.84x, with r ≈ 0.94, so about 88% of the variation in sales moves with footfall. Read the slope as a rate: each extra thousand people past the door is associated with roughly £1,840 a week in sales. Do not read the intercept — £2,140 at zero footfall — as a prediction, because no branch in the data comes close to zero.

The interesting part is what is left over. The branch at 4.2 sits about £1,310 above the line, and the one at 5.4 about £1,310 below. Those residuals are the question worth asking: two branches with similar traffic differ by £2,600 a week, and footfall does not explain it. Location, staffing, and product mix are the next things to plot. Note too that this says nothing about causation — a chain that puts its best-stocked branches in its busiest locations would produce exactly this chart.

To compare a single measure across branches rather than relate two, a bar chart is the right form; to see how those sales values are distributed on their own, try the histogram maker; and if your X axis is time rather than a second measurement, use the line chart maker.