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 |
an object of class |
data |
an optional data frame, list or environment (or object
coercible by |
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 |
na.action |
a function which indicates what should happen
when the data contain |
method |
the method to be used; for fitting, currently only
|
model , x , y , qr |
logicals. If |
singular.ok |
logical. If |
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.
This should be |
... |
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.
Non-NULL
weights
can be used to indicate that different
observations have different variances (with the values in
weights
being inversely proportional to the variances); or
equivalently, when the elements of weights
are positive
integers w_i
, that each response y_i
is the mean of
w_i
unit-weight observations (including the case that there are
w_i
observations equal to y_i
and the data have been
summarized).
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 |
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. |
na.action |
(where relevant) information returned by
|
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 NA
s would invalidate the time series
attributes, and if NA
s 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
.
biglm
in package biglm for an alternative
way to fit linear models to large datasets (especially those with many
cases).
require(graphics)
## 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