summary.lm               package:stats               R Documentation

Summarizing Linear Model Fits

Description:

     'summary' method for class '"lm"'.

Usage:

     ## S3 method for class 'lm':
     summary(object, correlation = FALSE, symbolic.cor = FALSE, ...)

     ## S3 method for class 'summary.lm':
     print(x, digits = max(3, getOption("digits") - 3),
           symbolic.cor = x$symbolic.cor,
           signif.stars = getOption("show.signif.stars"), ...)

Arguments:

  object: an object of class '"lm"', usually, a result of a call to
          'lm'.

       x: an object of class '"summary.lm"', usually, a result of a
          call to 'summary.lm'.

correlation: logical; if 'TRUE', the correlation matrix of the
          estimated parameters is returned and printed.

  digits: the number of significant digits to use when printing.

symbolic.cor: logical. If 'TRUE', print the correlations in a symbolic
          form (see 'symnum') rather than as numbers.

signif.stars: logical. If 'TRUE', 'significance stars' are printed for
          each coefficient.

     ...: further arguments passed to or from other methods.

Details:

     'print.summary.lm' tries to be smart about formatting the
     coefficients, standard errors, etc. and additionally gives
     'significance stars' if 'signif.stars' is 'TRUE'.

     Correlations are printed to two decimal places (or symbolically):
     to see the actual correlations print 'summary(object)$correlation'
     directly.

Value:

     The function 'summary.lm' computes and returns a list of summary
     statistics of the fitted linear model given in 'object', using the
     components (list elements) '"call"' and '"terms"' from its
     argument, plus 

residuals: the _weighted_ residuals, the usual residuals rescaled by
          the square root of the weights specified in the call to 'lm'.

coefficients: a 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.

 aliased: named logical vector showing if the original coefficients are
          aliased.

   sigma: the square root of the estimated variance of the random error

                 sigma^2 = 1/(n-p) Sum(w[i] R[i]^2),

          where R[i] is the i-th residual, 'residuals[i]'.

      df: degrees of freedom, a 3-vector (p, n-p, p*), the last being
          the number of non-aliased coefficients.

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.

r.squared: R^2, the 'fraction of variance explained by the model',

              R^2 = 1 - Sum(R[i]^2) / Sum((y[i]- y*)^2),

          where y* is the mean of y[i] if there is an intercept and
          zero otherwise.

adj.r.squared: the above R^2 statistic '_adjusted_', penalizing for
          higher p.

cov.unscaled: a p x p matrix of (unscaled) covariances of the coef[j],
          j=1, ..., p.

correlation: the correlation matrix corresponding to the above
          'cov.unscaled', if 'correlation = TRUE' is specified.

symbolic.cor: (only if 'correlation' is true.)  The value of the
          argument 'symbolic.cor'.

na.action: from 'object', if present there.

See Also:

     The model fitting function 'lm', 'summary'.

     Function 'coef' will extract the matrix of coefficients with
     standard errors, t-statistics and p-values.

Examples:

     ##-- 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

