Regression influential-point explorer

Every point is draggable, but the amber one sits far from the others in the x direction. Points like that have leverage, and leverage is power over the whole line.

line ŷ = 2.61 + 0.77xr 0.998r² 0.995
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residual plot (residual = actual y - predicted y)

Presets:the amber point has high leverage: drag it and watch r change

r = 0.998: a very strong positive linear relationship, and r-squared = 0.995 means the line explains 99.5% of the variation in y. Check the residual plot below: a pattern there means a line is the wrong model no matter how good r looks.

Try to:○ drag one point until r drops below 0.5○ make the relationship negative○ see the least squares (squares view)

What to try

  1. Influence. Drag the amber point straight down. The slope tips, r plunges, and every other point's residual changes even though none of them moved. One point, whole-line consequences: that is what influential means.
  2. Leverage vs influence. Drag a middle point down the same distance. The line barely reacts. Distance from the mean of x, not the size of the residual, is what gives a point its pull.
  3. Read the residual plot. Keep the points roughly linear and the residuals scatter randomly around zero. Bend the pattern into a curve and watch the residual plot bend too: the residual plot is where a bad model confesses.

The line is the least-squares fit, recomputed from scratch on every drag. For the formulas and interpretation language, see the least-squares regression line, r vs r-squared, and interpreting residual plots.

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