# summary.lm

##### Summarizing Linear Model Fits

`summary`

method for class `"lm"`

.

- Keywords
- models, regression

##### Usage

```
## S3 method for class 'lm':
summary(object, correlation = FALSE, symbolic.cor = FALSE, \dots)
```## 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
`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 residuals the *weighted*residuals, the usual residuals rescaled by the square root of the weights specified in the call to`lm`

.coefficients 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. aliased named logical vector showing if the original coefficients are aliased. sigma 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]`

.df 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. 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 , $$R^2 = 1 - \frac{\sum_i{R_i^2}}{\sum_i(y_i- y^*)^2},$$ where $y^*$ is the mean of $y_i$ if there is an intercept and zero otherwise.adj.r.squared the above $R^2$ statistic , penalizing for higher $p$.*adjusted*cov.unscaled a $p \times p$ matrix of (unscaled) covariances of the $\hat\beta_j$, $j=1, \dots, p$. 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

`library(stats)`

```
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))
```

*Documentation reproduced from package stats, version 3.3, License: Part of R 3.3*