Statistics

Least Squares

The best-fit line is the one that minimises the total squared error. Here each error is drawn as a literal square, so the line is quite literally the one that shrinks the total area the most.

Fit
Sum of squares
Points0

Drag any point to move it. Click empty space to add a point. The orange line is the least-squares fit; the shaded squares are the residuals, squared.

What to observe

  1. The fit line is exactly the one that makes the total area of the shaded squares as small as possible. Drag a point and watch the squares fight back.
  2. Drag one point far off the trend. Because errors are squared, that single outlier drags the whole line toward it: least squares is not robust.
  3. The line always pivots through the mean point (x̄, ȳ). Add points symmetrically and the slope changes while that balance point stays put.

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