# lm.ridge

From MASS v7.3-19
by Brian Ripley

##### Ridge Regression

Fit a linear model by ridge regression.

- Keywords
- models

##### Usage

```
lm.ridge(formula, data, subset, na.action, lambda = 0, model = FALSE,
x = FALSE, y = FALSE, contrasts = NULL, ...)
```

##### Arguments

- formula
- a formula expression as for regression models, of the form
`response ~ predictors`

. See the documentation of`formula`

for other details.`offset`

terms are allowed. - data
- an optional data frame in which to interpret the variables occurring
in
`formula`

. - subset
- expression saying which subset of the rows of the data should be used in the fit. All observations are included by default.
- na.action
- a function to filter missing data.
- lambda
- A scalar or vector of ridge constants.
- model
- should the model frame be returned? Not implemented.
- x
- should the design matrix be returned? Not implemented.
- y
- should the response be returned? Not implemented.
- contrasts
- a list of contrasts to be used for some or all of factor terms in the
formula. See the
`contrasts.arg`

of`model.matrix.default`

. - ...
- additional arguments to
`lm.fit`

.

##### Details

If an intercept is present in the model, its coefficient is not penalized. (If you want to penalize an intercept, put in your own constant term and remove the intercept.)

##### Value

- A list with components
coef matrix of coefficients, one row for each value of `lambda`

. Note that these are not on the original scale and are for use by the`coef`

method.scales scalings used on the X matrix. Inter was intercept included? lambda vector of lambda values ym mean of `y`

xm column means of `x`

matrixGCV vector of GCV values kHKB HKB estimate of the ridge constant. kLW L-W estimate of the ridge constant.

##### References

Brown, P. J. (1994)
*Measurement, Regression and Calibration*
Oxford.

##### See Also

##### Examples

```
longley # not the same as the S-PLUS dataset
names(longley)[1] <- "y"
lm.ridge(y ~ ., longley)
plot(lm.ridge(y ~ ., longley,
lambda = seq(0,0.1,0.001)))
select(lm.ridge(y ~ ., longley,
lambda = seq(0,0.1,0.0001)))
```

*Documentation reproduced from package MASS, version 7.3-19, License: GPL-2 | GPL-3*

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