# summary.lm

##### Summarizing Linear Model Fits

`summary`

method for class `"lm"`

.

- Keywords
- models, regression

##### Usage

```
# S3 method for lm
summary(object, correlation = FALSE, symbolic.cor = FALSE, …)
```# S3 method for 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`

.

Aliased coefficients are omitted in the returned object but restored
by the `print`

method.

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

the *weighted* residuals, the usual residuals
rescaled by the square root of the weights specified in the call to
`lm`

.

a \(p \times 4\) matrix with columns for the estimated coefficient, its standard error, t-statistic and corresponding (two-sided) p-value. Aliased coefficients are omitted.

named logical vector showing if the original coefficients are aliased.

the square root of the estimated variance of the random
error
$$\hat\sigma^2 = \frac{1}{n-p}\sum_i{w_i R_i^2},$$
where \(R_i\) is the \(i\)-th residual, `residuals[i]`

.

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

(for models including non-intercept terms) a 3-vector with the value of the F-statistic with its numerator and denominator degrees of freedom.

\(R^2\), the ‘fraction of variance explained by the model’, $$R^2 = 1 - \frac{\sum_i{R_i^2}}{\sum_i(y_i- y^*)^2},$$ where \(y^*\) is the mean of \(y_i\) if there is an intercept and zero otherwise.

the above \(R^2\) statistic
‘*adjusted*’, penalizing for higher \(p\).

a \(p \times p\) matrix of (unscaled) covariances of the \(\hat\beta_j\), \(j=1, \dots, p\).

the correlation matrix corresponding to the above
`cov.unscaled`

, if `correlation = TRUE`

is specified.

(only if `correlation`

is true.) The value
of the argument `symbolic.cor`

.

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

`library(stats)`

```
# NOT RUN {
##-- 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))
# }
```

*Documentation reproduced from package stats, version 3.5.3, License: Part of R 3.5.3*