# lm.ridge

##### 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

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.

scalings used on the X matrix.

was intercept included?

vector of lambda values

mean of `y`

column means of `x`

matrix

vector of GCV values

HKB estimate of the ridge constant.

L-W estimate of the ridge constant.

##### References

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

##### See Also

##### Examples

```
# NOT RUN {
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 7.3-51.5, License: GPL-2 | GPL-3*