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Mathematics
Find a line that fits the data
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Drag the line close to the points
6/100 points
y = 0x + 10
y =0slopex +10meets the y-axis
What to show
- Yours
- 0.24
- Best fit
- 0.012
19× the least total
Smaller square = closer line
- Correlation r
- 0.973
−1 · falling01 · rising
Why squares?
A residual is the vertical distance from a point to the line. Squaring prevents positive and negative residuals from canceling. The best-fit line minimizes their total. Totals are measured with the graph's height as one unit, so data sets can be compared.
Model notes
- Least squares minimizes vertical squared residuals, not perpendicular distances. A correlation alone does not establish cause and effect.
- Computations use a graph normalized to 0–1 on both axes, as do the squared-error comparisons. Slope, y-intercept, equations and point coordinates are shown in the data's original units; the model limits apply on the normalized scale: slope from −10 to 10, intercept from −1.5 to 1.5.
- A best-fit line needs at least two points with sufficient variation in x. Correlation is undefined for constant data. Near-singular cases use numerical thresholds instead of displaying unstable values.
- The provided historical data sets retain their original values and references. They are examples for exploring fitting, not current measurements. Custom data is limited to 100 points to keep touch editing manageable.