| lm {base} | R Documentation |
Fitting Linear Models
Description
lm is used to fit linear models.
It can be used to carry out regression,
single stratum analysis of variance and
analysis of covariance (although aov may provide a more
convenient interface for these).
Usage
lm(formula, data, subset, weights, na.action,
method = "qr", model = TRUE, x = FALSE, y = FALSE, qr = TRUE,
singular.ok = TRUE contrasts = NULL, offset = NULL, ...)
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
formula |
a symbolic description of the model to be fit. The details of model specification are given below. |
data |
an optional data frame containing the variables
in the model. By default the variables are taken from
the environment which |
subset |
an optional vector specifying a subset of observations to be used in the fitting process. |
weights |
an optional vector of weights to be used
in the fitting process. If specified, weighted least squares is used
with weights |
na.action |
a function which indicates what should happen
when the data contain |
model, x, y, qr |
logicals. If |
singular.ok |
logical, defaulting to
|
method |
currently, only |
contrasts |
an optional list. See the |
offset |
this can be used to specify an a priori
known component to be included in the linear predictor
during fitting. An |
tol |
tolerance for the |
... |
currently disregarded. |
Details
Models for lm are specified symbolically. A typical model has
the form response ~ terms where response is the (numeric)
response vector and terms is a series of terms which specifies a
linear predictor for response. A terms specification of the form
first+second indicates all the terms in first together
with all the terms in second with duplicates removed. A
specification of the form first:second indicates the the set of
terms obtained by taking the interactions of all terms in first
with all terms in second. The specification first*second
indicates the cross of first and second. This is
the same as first+second+first:second.
Value
lm returns an object of class "lm" or for
multiple responses of class c("mlm", "lm").
The functions summary and anova are used to
obtain and print a summary and analysis of variance table of the results.
The generic accessor functions coefficients,
effects, fitted.values and residuals
extract various useful features of the value returned by lm.
Note
Offsets specified by offset will not be included in predictions
by predict.lm, whereas those specified by an offset term
in the formula will be.
See Also
summary.lm for summaries and anova.lm for
the ANOVA table; aov for a different interface.
The generic functions coefficients, effects,
residuals, fitted.values.
predict.lm (via predict(..)) for prediction,
including confidence and prediction intervals.
lm.influence for regression diagnostics, and
glm for generalized linear models.
Examples
## Annette Dobson (1990) "An Introduction to Generalized Linear Models".
## Page 9: Plant Weight Data.
ctl <- c(4.17,5.58,5.18,6.11,4.50,4.61,5.17,4.53,5.33,5.14)
trt <- c(4.81,4.17,4.41,3.59,5.87,3.83,6.03,4.89,4.32,4.69)
group <- gl(2,10,20, labels=c("Ctl","Trt"))
weight <- c(ctl, trt)
anova(lm.D9 <- lm(weight ~ group))
summary(lm.D90 <- lm(weight ~ group - 1))# omitting intercept
summary(resid(lm.D9) - resid(lm.D90)) #- residuals almost identical
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(lm.D9, las = 1) # Residuals, Fitted, ...
par(opar)