| % File src/library/stats/man/summary.lm.Rd |
| % Part of the R package, https://www.R-project.org |
| % Copyright 1995-2013 R Core Team |
| % Distributed under GPL 2 or later |
| |
| \name{summary.lm} |
| \alias{summary.lm} |
| \alias{summary.mlm}% mlm is *not* mentioned at all |
| \alias{print.summary.lm} |
| \title{Summarizing Linear Model Fits} |
| \usage{ |
| \method{summary}{lm}(object, correlation = FALSE, symbolic.cor = FALSE, \dots) |
| |
| \method{print}{summary.lm}(x, digits = max(3, getOption("digits") - 3), |
| symbolic.cor = x$symbolic.cor, |
| signif.stars = getOption("show.signif.stars"), \dots) |
| } |
| \arguments{ |
| \item{object}{an object of class \code{"lm"}, usually, a result of a |
| call to \code{\link{lm}}.} |
| \item{x}{an object of class \code{"summary.lm"}, usually, a result of a |
| call to \code{summary.lm}.} |
| \item{correlation}{logical; if \code{TRUE}, the correlation matrix of |
| the estimated parameters is returned and printed.} |
| \item{digits}{the number of significant digits to use when printing.} |
| \item{symbolic.cor}{logical. If \code{TRUE}, print the correlations in |
| a symbolic form (see \code{\link{symnum}}) rather than as numbers.} |
| \item{signif.stars}{logical. If \code{TRUE}, \sQuote{significance stars} |
| are printed for each coefficient.} |
| \item{\dots}{further arguments passed to or from other methods.} |
| } |
| \description{ |
| \code{summary} method for class \code{"lm"}. |
| } |
| \details{ |
| \code{print.summary.lm} tries to be smart about formatting the |
| coefficients, standard errors, etc. and additionally gives |
| \sQuote{significance stars} if \code{signif.stars} is \code{TRUE}. |
| |
| Aliased coefficients are omitted in the returned object but restored |
| by the \code{print} method. |
| |
| Correlations are printed to two decimal places (or symbolically): to |
| see the actual correlations print \code{summary(object)$correlation} |
| directly. |
| } |
| \value{ |
| The function \code{summary.lm} computes and returns a list of summary |
| statistics of the fitted linear model given in \code{object}, using |
| the components (list elements) \code{"call"} and \code{"terms"} |
| from its argument, plus |
| \item{residuals}{the \emph{weighted} residuals, the usual residuals |
| rescaled by the square root of the weights specified in the call to |
| \code{lm}.} |
| \item{coefficients}{a \eqn{p \times 4}{p x 4} matrix with columns for |
| the estimated coefficient, its standard error, t-statistic and |
| corresponding (two-sided) p-value. Aliased coefficients are omitted.} |
| \item{aliased}{named logical vector showing if the original |
| coefficients are aliased.} |
| \item{sigma}{the square root of the estimated variance of the random |
| error |
| \deqn{\hat\sigma^2 = \frac{1}{n-p}\sum_i{w_i R_i^2},}{\sigma^2 = 1/(n-p) Sum(w[i] R[i]^2),} |
| where \eqn{R_i}{R[i]} is the \eqn{i}-th residual, \code{residuals[i]}.} |
| \item{df}{degrees of freedom, a 3-vector \eqn{(p, n-p, p*)}, the first |
| being the number of non-aliased coefficients, the last being the total |
| number of coefficients.} |
| \item{fstatistic}{(for models including non-intercept terms) |
| a 3-vector with the value of the F-statistic with |
| its numerator and denominator degrees of freedom.} |
| \item{r.squared}{\eqn{R^2}, the \sQuote{fraction of variance explained by |
| the model}, |
| \deqn{R^2 = 1 - \frac{\sum_i{R_i^2}}{\sum_i(y_i- y^*)^2},}{R^2 = 1 - Sum(R[i]^2) / Sum((y[i]- y*)^2),} |
| where \eqn{y^*}{y*} is the mean of \eqn{y_i}{y[i]} if there is an |
| intercept and zero otherwise.} |
| \item{adj.r.squared}{the above \eqn{R^2} statistic |
| \sQuote{\emph{adjusted}}, penalizing for higher \eqn{p}.} |
| \item{cov.unscaled}{a \eqn{p \times p}{p x p} matrix of (unscaled) |
| covariances of the \eqn{\hat\beta_j}{coef[j]}, \eqn{j=1, \dots, p}.} |
| \item{correlation}{the correlation matrix corresponding to the above |
| \code{cov.unscaled}, if \code{correlation = TRUE} is specified.} |
| \item{symbolic.cor}{(only if \code{correlation} is true.) The value |
| of the argument \code{symbolic.cor}.} |
| \item{na.action}{from \code{object}, if present there.} |
| } |
| \seealso{ |
| The model fitting function \code{\link{lm}}, \code{\link{summary}}. |
| |
| Function \code{\link{coef}} will extract the matrix of coefficients |
| with standard errors, t-statistics and p-values. |
| } |
| \examples{ |
| \dontshow{utils::example("lm", echo = FALSE)} |
| ##-- Continuing the lm(.) example: |
| coef(lm.D90) # the bare coefficients |
| sld90 <- summary(lm.D90 <- lm(weight ~ group -1)) # omitting intercept |
| sld90 |
| coef(sld90) # much more |
| |
| ## model with *aliased* coefficient: |
| lm.D9. <- lm(weight ~ group + I(group != "Ctl")) |
| Sm.D9. <- summary(lm.D9.) |
| Sm.D9. # shows the NA NA NA NA line |
| stopifnot(length(cc <- coef(lm.D9.)) == 3, is.na(cc[3]), |
| dim(coef(Sm.D9.)) == c(2,4), Sm.D9.$df == c(2, 18, 3)) |
| } |
| \keyword{regression} |
| \keyword{models} |