| lm {base} | 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 = 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, ...)
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 lm is called from. |
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 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. |
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, defaulting to
TRUE. FALSE is not yet implemented. |
method |
currently, only method="qr" is supported. |
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. An offset term can be included in the
formula instead or as well, and if both are specified their sum is used. |
tol |
tolerance for the qr decomposition. Default
is 1e-7. |
... |
currently disregarded. |
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.
lm returns an object of class "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.
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.
summary.lm for summaries and anova.lm for
the ANOVA table. aov for a different interface.
The generic functions coefficients, effects,
residuals, fitted.values;
lm.influence for regression diagnostics, and
glm for generalized linear models.
## 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)