| lm {stats} | R Documentation |
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).
lm(formula, data, subset, weights, na.action, method = "qr", model = TRUE, x = FALSE, y = FALSE, qr = TRUE, singular.ok = TRUE, contrasts = NULL, offset, ...)
formula |
a symbolic description of the model to be fit. The details of model specification are given below. |
data |
an optional data frame, list or environment (or object
coercible by as.data.frame to a data frame) containing
the variables in the model. If not found in data, the
variables are taken from environment(formula),
typically the environment from which lm is called. |
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. Should be NULL or a numeric vector.
If non-NULL, weighted least squares is used with weights
weights (that is, minimizing sum(w*e^2)); otherwise
ordinary least squares is used. |
na.action |
a function which indicates what should happen
when the data contain NAs. The default is set by
the na.action setting of options, and is
na.fail if that is unset. The “factory-fresh”
default is na.omit. Another possible value is
NULL, no action. Value na.exclude can be useful. |
method |
the method to be used; for fitting, currently only
method = "qr" is supported; method = "model.frame" returns
the model frame (the same as with model = TRUE, see below). |
model, x, y, qr |
logicals. If TRUE the corresponding
components of the fit (the model frame, the model matrix, the
response, the QR decomposition) are returned.
|
singular.ok |
logical. If FALSE (the default in S but
not in R) a singular fit is an error. |
contrasts |
an optional list. See the contrasts.arg
of model.matrix.default. |
offset |
this can be used to specify an a priori
known component to be included in the linear predictor
during fitting. This should be NULL or a numeric vector of
length either one or equal to the number of cases.
One or more offset terms can be included in the
formula instead or as well, and if both are specified their sum is
used. See model.offset. |
... |
additional arguments to be passed to the low level regression fitting functions (see below). |
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 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.
If the formula includes an offset, this is evaluated and
subtracted from the response.
If response is a matrix a linear model is fitted separately by
least-squares to each column of the matrix.
See model.matrix for some further details. The terms in
the formula will be re-ordered so that main effects come first,
followed by the interactions, all second-order, all third-order and so
on: to avoid this pass a terms object as the formula (see
aov and demo(glm.vr) for an example).
A formula has an implied intercept term. To remove this use either
y ~ x - 1 or y ~ 0 + x. See formula for
more details of allowed formulae.
lm calls the lower level functions lm.fit, etc,
see below, for the actual numerical computations. For programming
only, you may consider doing likewise.
All of weights, subset and offset are evaluated
in the same way as variables in formula, that is first in
data and then in the environment of formula.
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.
An object of class "lm" is a list containing at least the
following components:
coefficients |
a named vector of coefficients |
residuals |
the residuals, that is response minus fitted values. |
fitted.values |
the fitted mean values. |
rank |
the numeric rank of the fitted linear model. |
weights |
(only for weighted fits) the specified weights. |
df.residual |
the residual degrees of freedom. |
call |
the matched call. |
terms |
the terms object used. |
contrasts |
(only where relevant) the contrasts used. |
xlevels |
(only where relevant) a record of the levels of the factors used in fitting. |
offset |
the offset used (missing if none were used). |
y |
if requested, the response used. |
x |
if requested, the model matrix used. |
model |
if requested (the default), the model frame used. |
In addition, non-null fits will have components assign,
effects and (unless not requested) qr relating to the linear
fit, for use by extractor functions such as summary and
effects.
Considerable care is needed when using lm with time series.
Unless na.action = NULL, the time series attributes are
stripped from the variables before the regression is done. (This is
necessary as omitting NAs would invalidate the time series
attributes, and if NAs are omitted in the middle of the series
the result would no longer be a regular time series.)
Even if the time series attributes are retained, they are not used to
line up series, so that the time shift of a lagged or differenced
regressor would be ignored. It is good practice to prepare a
data argument by ts.intersect(..., dframe = TRUE),
then apply a suitable na.action to that data frame and call
lm with na.action = NULL so that residuals and fitted
values are time series.
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.
The design was inspired by the S function of the same name described in Chambers (1992). The implementation of model formula by Ross Ihaka was based on Wilkinson & Rogers (1973).
Chambers, J. M. (1992) Linear models. Chapter 4 of Statistical Models in S eds J. M. Chambers and T. J. Hastie, Wadsworth & Brooks/Cole.
Wilkinson, G. N. and Rogers, C. E. (1973) Symbolic descriptions of factorial models for analysis of variance. Applied Statistics, 22, 392–9.
summary.lm for summaries and anova.lm for
the ANOVA table; aov for a different interface.
The generic functions coef, effects,
residuals, fitted, vcov.
predict.lm (via predict) for prediction,
including confidence and prediction intervals;
confint for confidence intervals of parameters.
lm.influence for regression diagnostics, and
glm for generalized linear models.
The underlying low level functions,
lm.fit for plain, and lm.wfit for weighted
regression fitting.
More lm() examples are available e.g., in
anscombe,
attitude,
freeny,
LifeCycleSavings,
longley,
stackloss,
swiss.
## 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)
## model frame :
stopifnot(identical(lm(weight ~ group, method = "model.frame"),
model.frame(lm.D9)))
### less simple examples in "See Also" above