Normal Distribution
nothing is called 95% until it has been counted
Concept

Cook's distance — where it appears

The summed squared movement of every fitted value when one row is deleted, scaled by the parameter count and the error variance. It is the squared residual times a function of leverage, so it comes from the full fit alone, and it measures one row at a time.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Twenty points and one more, at leverage 0.74. Without the distant point the slope is 0.495; with it the slope is -0.389. Its leverage is 0.737 and its Cook's distance is 24.1, against a conventional threshold of 1.

The line that one point drew

A single observation among twenty-one reverses the sign of a fitted relationship. Its leverage is known from its x value before the outcome is looked at, so this is a property of the design rather than a surprise in the data.

regression · Leverage Two far rows, and the line with one of them deleted. Twenty clean points and two rows near x = 9. The slope is −0.511 with every row, −0.376 with one far row deleted, and 0.495 with both deleted. Deleting one of them barely moves the line, because the other is still there.

Two points that hide each other

One far observation among twenty-one has a Cook's distance of 24.1. Put a second beside it and the two read 0.966 and 0.772, neither crossing 1, while together they reverse the slope and deleting both moves the fit by 53.3.

regression · Leverage

Named alongside it

The objects these essays reach for when they reach for this one.

InfluenceLeast squaresLeverageOutliersBonferroniClosed formGroup deletionHat matrixLeave-one-outMaskingModel diagnosticsStudentised residual

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