Six plots (selectable by `which`

) are currently available: a plot
of residuals against fitted values, a Scale-Location plot of
\(\sqrt{| residuals |}\)
against fitted values, a Normal Q-Q plot, a
plot of Cook's distances versus row labels, a plot of residuals
against leverages, and a plot of Cook's distances against
leverage/(1-leverage). By default, the first three and `5`

are
provided.

```
# S3 method for lm
plot(x, which = c(1,2,3,5),
caption = list("Residuals vs Fitted", "Normal Q-Q",
"Scale-Location", "Cook's distance",
"Residuals vs Leverage",
expression("Cook's dist vs Leverage " * h[ii] / (1 - h[ii]))),
panel = if(add.smooth) function(x, y, ...)
panel.smooth(x, y, iter=iter.smooth, ...) else points,
sub.caption = NULL, main = "",
ask = prod(par("mfcol")) < length(which) && dev.interactive(),
…,
id.n = 3, labels.id = names(residuals(x)), cex.id = 0.75,
qqline = TRUE, cook.levels = c(0.5, 1.0),
add.smooth = getOption("add.smooth"),
iter.smooth = if(isGlm && binomialLike) 0 else 3,
label.pos = c(4,2),
cex.caption = 1, cex.oma.main = 1.25)
```

which

if a subset of the plots is required, specify a subset of
the numbers `1:6`

, see `caption`

below (and the
‘Details’) for the different kinds.

caption

captions to appear above the plots;
`character`

vector or `list`

of valid
graphics annotations, see `as.graphicsAnnot`

, of length
6, the j-th entry corresponding to `which[j]`

. Can be set to
`""`

or `NA`

to suppress all captions.

panel

panel function. The useful alternative to
`points`

, `panel.smooth`

can be chosen
by `add.smooth = TRUE`

.

sub.caption

common title---above the figures if there are more
than one; used as `sub`

(s.`title`

) otherwise. If
`NULL`

, as by default, a possible abbreviated version of
`deparse(x$call)`

is used.

main

title to each plot---in addition to `caption`

.

ask

logical; if `TRUE`

, the user is *ask*ed before
each plot, see `par(ask=.)`

.

…

other parameters to be passed through to plotting functions.

id.n

number of points to be labelled in each plot, starting with the most extreme.

labels.id

vector of labels, from which the labels for extreme
points will be chosen. `NULL`

uses observation numbers.

cex.id

magnification of point labels.

qqline

logical indicating if a `qqline()`

should be
added to the normal Q-Q plot.

cook.levels

levels of Cook's distance at which to draw contours.

add.smooth

logical indicating if a smoother should be added to
most plots; see also `panel`

above.

iter.smooth

the number of robustness iterations, the argument
`iter`

in `panel.smooth()`

; the default uses no such
iterations for `glm(*, family=binomial)`

fits which is
particularly desirable for the (predominant) case of binary observations.

label.pos

positioning of labels, for the left half and right half of the graph respectively, for plots 1-3.

cex.caption

controls the size of `caption`

.

cex.oma.main

controls the size of the `sub.caption`

only if
that is *above* the figures when there is more than one.

`sub.caption`

---by default the function call---is shown as
a subtitle (under the x-axis title) on each plot when plots are on
separate pages, or as a subtitle in the outer margin (if any) when
there are multiple plots per page.

The ‘Scale-Location’ plot, also called ‘Spread-Location’ or ‘S-L’ plot, takes the square root of the absolute residuals in order to diminish skewness (\(\sqrt{| E |}\) is much less skewed than \(| E |\) for Gaussian zero-mean \(E\)).

The ‘S-L’, the Q-Q, and the Residual-Leverage plot, use
*standardized* residuals which have identical variance (under the
hypothesis). They are given as
\(R_i / (s \times \sqrt{1 - h_{ii}})\)
where \(h_{ii}\) are the diagonal entries of the hat matrix,
`influence()$hat`

(see also `hat`

), and
where the Residual-Leverage plot uses standardized Pearson residuals
(`residuals.glm(type = "pearson")`

) for \(R[i]\).

The Residual-Leverage plot shows contours of equal Cook's distance,
for values of `cook.levels`

(by default 0.5 and 1) and omits
cases with leverage one with a warning. If the leverages are constant
(as is typically the case in a balanced `aov`

situation)
the plot uses factor level combinations instead of the leverages for
the x-axis. (The factor levels are ordered by mean fitted value.)

In the Cook's distance vs leverage/(1-leverage) plot, contours of
standardized residuals (`rstandard(.)`

) that are equal in
magnitude are lines through the origin. The contour lines are
labelled with the magnitudes.

Belsley, D. A., Kuh, E. and Welsch, R. E. (1980).
*Regression Diagnostics*.
New York: Wiley.

Cook, R. D. and Weisberg, S. (1982).
*Residuals and Influence in Regression*.
London: Chapman and Hall.

Firth, D. (1991) Generalized Linear Models. In Hinkley, D. V. and Reid, N. and Snell, E. J., eds: Pp.55-82 in Statistical Theory and Modelling. In Honour of Sir David Cox, FRS. London: Chapman and Hall.

Hinkley, D. V. (1975).
On power transformations to symmetry.
*Biometrika*, **62**, 101--111.
10.2307/2334491.

McCullagh, P. and Nelder, J. A. (1989).
*Generalized Linear Models*.
London: Chapman and Hall.

# NOT RUN { require(graphics) ## Analysis of the life-cycle savings data ## given in Belsley, Kuh and Welsch. lm.SR <- lm(sr ~ pop15 + pop75 + dpi + ddpi, data = LifeCycleSavings) plot(lm.SR) ## 4 plots on 1 page; ## allow room for printing model formula in outer margin: par(mfrow = c(2, 2), oma = c(0, 0, 2, 0)) plot(lm.SR) plot(lm.SR, id.n = NULL) # no id's plot(lm.SR, id.n = 5, labels.id = NULL) # 5 id numbers ## Was default in R <= 2.1.x: ## Cook's distances instead of Residual-Leverage plot plot(lm.SR, which = 1:4) ## Fit a smooth curve, where applicable: plot(lm.SR, panel = panel.smooth) ## Gives a smoother curve plot(lm.SR, panel = function(x, y) panel.smooth(x, y, span = 1)) par(mfrow = c(2,1)) # same oma as above plot(lm.SR, which = 1:2, sub.caption = "Saving Rates, n=50, p=5") # }