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" (or one that
can be coerced to that class): a symbolic description of the
model to be fitted. The details of model specification are given
under ‘Details’.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.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. See also ‘Details’,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 = "qr" is supported; method = "model.frame" returns
the model frame (the same as with model = TRUE, see below).TRUE the corresponding
components of the fit (the model frame, the model matrix, the
response, the QR decomposition) are returned.
FALSE (the default in S but
not in R) a singular fit is an error.contrasts.arg
of model.matrix.default.NULL or a numeric vector of length equal to
the number of cases. One or more offset terms can be
included in the formula instead or as well, and if more than one are
specified their sum is used. See model.offset.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: terms object used.model.frame on the special handling of NAs.assign,
effects and (unless not requested) qr relating to the linear
fit, for use by extractor functions such as summary and
effects.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.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.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 https://CRAN.R-project.org/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)
lm.D9 <- lm(weight ~ group)
lm.D90 <- lm(weight ~ group - 1) # omitting intercept
anova(lm.D9)
summary(lm.D90)
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(lm.D9, las = 1) # Residuals, Fitted, ...
par(opar)
### less simple examples in "See Also" above
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