leverage

Syntax

h = leverage(data)
h = leverage(data,model)

Description

h = leverage(data) finds the leverage of each row (point) in the matrix data for a linear additive regression model.

h = leverage(data,model) finds the leverage on a regression, using a specified model type, where model can be one of these strings:

  • 'linear' - includes constant and linear terms

  • 'interaction' - includes constant, linear, and cross product terms

  • 'quadratic' - includes interactions and squared terms

  • 'purequadratic' - includes constant, linear, and squared terms

Leverage is a measure of the influence of a given observation on a regression due to its location in the space of the inputs.

Examples

One rule of thumb is to compare the leverage to 2p/n where n is the number of observations and p is the number of parameters in the model. For the Hald data set this value is 0.7692.

load hald
h = max(leverage(ingredients,'linear'))
h =
  0.7004

Since 0.7004 < 0.7692, there are no high leverage points using this rule.

More About

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Algorithms

[Q,R] = qr(x2fx(data,'model'));

leverage = (sum(Q'.*Q'))'

References

[1] Goodall, C. R. "Computation Using the QR Decomposition." Handbook in Statistics. Vol. 9, Amsterdam: Elsevier/North-Holland, 1993.

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