R: Fitter Functions for Linear Models

lm.fit {base} | R Documentation

## Fitter Functions for Linear Models

### Description

These are the basic computing engines called by `lm` used to fit linear models. These should usually not be used directly unless by experienced users.

### Usage

    lm.fit (x, y,    offset = NULL, method = "qr", tol = 1e-7, ...)
    lm.wfit(x, y, w, offset = NULL, method = "qr", tol = 1e-7, ...)
    lm.fit.null (x, y,    method = "qr", tol = 1e-7, ...)
    lm.wfit.null(x, y, w, method = "qr", tol = 1e-7, ...)

### Arguments

`x` | design matrix of dimension `n * p`.
`y` | vector of observations of length `n`.
`w` | vector of weights (length `n`) to be used in the fitting process for the `wfit` functions. Weighted least squares is used with weights `w`, i.e., `sum(w * e^2)` is minimized.
`offset` | numeric of length `n`). This can be used to specify an a priori known component to be included in the linear predictor during fitting.
`method` | currently, only `method="qr"` is supported.
`tol` | tolerance for the `qr` decomposition. Default is 1e-7.
`...` | currently disregarded.

### Details

The functions `lm.{w}fit.null` are called by `lm.fit` or `lm.wfit` respectively, when `x` has zero columns.

### Value

a list with components

`coefficients` | `p` vector
`residuals` | `n` vector
`fitted.values` | `n` vector
`effects` | `n` vector; ......
`weights` | `n` vector — only for the `*wfit*` functions.
`rank` | integer, giving the rank
`df.residual` | degrees of freedom of residuals
`qr` | the QR decomposition, see `qr`.

### See Also

`lm` which you should use for linear least squares regression, unless you know better.

### Examples

    set.seed(129)
    n <- 7 ; p <- 2
    X <- matrix(rnorm(n * p), n,p) # no intercept!
    y <- rnorm(n)
    w <- rnorm(n)^2

    str(lmw <- lm.wfit(x=X, y=y, w=w))

    str(lm. <- lm.fit (x=X, y=y))

    str(lm0 <-  lm.fit.null (x=X, y=y))
    str(lmw0 <- lm.wfit.null(x=X, y=y,w=w))

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