Statistics Toolbox

leverage

Leverage values for a regression

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.

Example

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 dataset 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.

Algorithm

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

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

Reference

[1]  Goodall, C. R. (1993). Computation using the QR decomposition. Handbook in Statistics, Volume 9. Statistical Computing (C. R. Rao, ed.). Amsterdam, NL Elsevier/North-Holland.

See Also
regstats

kurtosis

lhsdesign