# Documentation

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# 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 the following:

• `'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.

## 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.