Scatter plot maker, with a trend line.

A scatter plot maker draws one dot for every pair of numbers, with the first number across and the second one up. The shape of the cloud shows whether the two things move together. This one draws the plot as you type, can split the dots into groups by colour, and fits a trend line with its equation and R squared, so you can say how strong the link is as well as show it.

How to use the scatter plot maker

1. Type a Title, or clear the box to draw the plot without one.
2. Put your numbers in the Data box, one pair on each line: the x value, then the y value, like 3 61. A tab, comma, semicolon or space between them all work, so you can paste straight from a spreadsheet. You can also click Open a CSV file, or drop a file on the box.
3. If the first row holds names, such as Hours studied and Test score, they become the axis titles. You can still type your own under X axis title and Y axis title.
4. To make groups, add a third column of text, like A or B. Each group gets its own colour and its own entry in the legend. Tick A different shape for each group if the plot will be printed in black and white.
5. Under Fit, pick Straight line, Curve, degree 2 or Curve, degree 3. The equation and R² show on the plot and in the table under it. Copy equations puts them on the clipboard.
6. Change Point size, the colours, the background and the grid. Use X from, X to, Y from and Y to to set your own range, and the log scale switches for data that grows by multiples.
7. Click Save PNG, or use Copy picture, SVG or PDF.

How the trend line is worked out

The straight line is the least squares line: the one that makes the sum of the squared vertical gaps between the dots and the line as small as it can be. Its slope is the sum of (x minus the mean of x) times (y minus the mean of y), divided by the sum of (x minus the mean of x) squared. The intercept is the mean of y minus the slope times the mean of x.

Take the example that loads with the tool: hours studied from 1 to 10 against a test score. The mean of x is 5.5 and the mean of y is 68.8. The slope works out to 3.903 and the intercept to 47.33, so the line is y = 3.903x + 47.33. Each extra hour goes with about 3.9 more points. The curves of degree 2 and 3 are fitted the same way, with an x squared term, and an x cubed term as well.

What R² and r tell you

R² is the share of the ups and downs in y that the trend line accounts for. It is 1 minus the leftover squared gap divided by the total squared gap around the mean of y. An R² of 0.9685 on the example means the line accounts for about 97% of the variation in the scores. For a straight line, r is the square root of R², with the sign of the slope: 0.9841 here.

A higher degree always fits the same points at least as well, so R² can only go up. Here it barely does, so the straight line is the better description. Use a curve when the dots visibly bend, as in the A curve example, where a line gives an R² of 0.9373 and degree 2 gives 0.9999.

Groups, one line or many

With two or more groups, One trend line for each group fits each colour on its own. Untick it to fit all the points together. In the Two groups example, groups A and B each have a tight line (R² of 0.9925 and 0.9945), but fitted together the R² drops to 0.7231, because the groups sit at different heights. That is a good reason to look at the groups before trusting one overall line.

Log axes

A log scale puts equal multiples at equal distances: 1, 10, 100 are evenly spaced. It suits data that spans many orders of size. Zero and negative numbers cannot be drawn on a log axis, so the tool leaves those points out and tells you how many. The trend line is fitted to the numbers as typed and then drawn on the log axis, so it bends there.

Common problems

• Some lines are skipped: a line needs two numbers at the start. The note under the plot says how many were left out.
• The trend line says it needs more points: a line needs two different x values, degree 2 needs three, degree 3 needs four.
• A correlation is not a cause. A trend line describes the points you gave it and says nothing on why they line up.

For counts and shares of a whole, try the pie chart maker or the bar graph maker. To plot a formula instead of data, use the graphing calculator.