Plots empirical quantiles of a variable, or of studentized residuals from
a linear model, against theoretical quantiles of a comparison distribution. Includes
options not available in the `qqnorm`

function.

`qqPlot(x, ...)`qqp(...)

# S3 method for default
qqPlot(x, distribution="norm", groups, layout,
ylim=range(x, na.rm=TRUE), ylab=deparse(substitute(x)),
xlab=paste(distribution, "quantiles"), glab=deparse(substitute(groups)),
main=NULL, las=par("las"),
envelope=TRUE, col=carPalette()[1], col.lines=carPalette()[2],
lwd=2, pch=1, cex=par("cex"),
line=c("quartiles", "robust", "none"), id=TRUE, grid=TRUE, ...)

# S3 method for formula
qqPlot(formula, data, subset, id=TRUE, ylab, glab, ...)

# S3 method for lm
qqPlot(x, xlab=paste(distribution, "Quantiles"),
ylab=paste("Studentized Residuals(",
deparse(substitute(x)), ")", sep=""),
main=NULL, distribution=c("t", "norm"),
line=c("robust", "quartiles", "none"), las=par("las"),
simulate=TRUE, envelope=TRUE, reps=100,
col=carPalette()[1], col.lines=carPalette()[2], lwd=2, pch=1, cex=par("cex"),
id=TRUE, grid=TRUE, ...)

These functions return the labels of identified points, unless a grouping factor is employed,
in which case `NULL`

is returned invisibly.

- x
vector of numeric values or

`lm`

object.- distribution
root name of comparison distribution -- e.g.,

`"norm"`

for the normal distribution;`t`

for the t-distribution.- groups
an optional factor; if specified, a QQ plot will be drawn for

`x`

within each level of`groups`

.- layout
a 2-vector with the number of rows and columns for plotting by groups -- for example

`c(1, 3)`

for 1 row and 3 columns; if omitted, the number of rows and columns will be selected automatically; the specified number of rows and columns must be sufficient to accomodate the number of groups; ignored if there is no grouping factor.- formula
one-sided formula specifying a single variable to be plotted or a two-sided formula of the form

`variable ~ factor`

, where a QQ plot will be drawn for`variable`

within each level of`factor`

.- data
optional data frame within which to evaluage the formula.

- subset
optional subset expression to select cases to plot.

- ylim
limits for vertical axis; defaults to the range of

`x`

. If plotting by groups, a common y-axis is used for all groups.- ylab
label for vertical (empirical quantiles) axis.

- xlab
label for horizontal (comparison quantiles) axis.

- glab
label for the grouping variable.

- main
label for plot.

- envelope
`TRUE`

(the default),`FALSE`

, a confidence level such as`0.95`

, or a list specifying how to plot a point-wise confidence envelope (see Details).- las
if

`0`

, ticks labels are drawn parallel to the axis; set to`1`

for horizontal labels (see`par`

).- col
color for points; the default is the

*first*entry in the current car palette (see`carPalette`

and`par`

).- col.lines
color for lines; the default is the

*second*entry in the current car palette.- pch
plotting character for points; default is

`1`

(a circle, see`par`

).- cex
factor for expanding the size of plotted symbols; the default is

`1`

.- id
controls point identification; if

`FALSE`

, no points are identified; can be a list of named arguments to the`showLabels`

function;`TRUE`

is equivalent to`list(method="y", n=2, cex=1, col=carPalette()[1], location="lr")`

, which identifies the 2 points with the 2 points with the most extreme verical values --- studentized residuals for the`"lm"`

method. Points labels are by default taken from the names of the variable being plotted is any, else case indices are used. Unlike most graphical functions in car, the default is`id=TRUE`

to include point identification.- lwd
line width; default is

`2`

(see`par`

).- line
`"quartiles"`

to pass a line through the quartile-pairs, or`"robust"`

for a robust-regression line; the latter uses the`rlm`

function in the`MASS`

package. Specifying`line = "none"`

suppresses the line.- simulate
if

`TRUE`

calculate confidence envelope by parametric bootstrap; for`lm`

object only. The method is due to Atkinson (1985).- reps
integer; number of bootstrap replications for confidence envelope.

- ...
arguments such as

`df`

to be passed to the appropriate quantile function.- grid
If TRUE, the default, a light-gray background grid is put on the graph

John Fox jfox@mcmaster.ca

Draws theoretical quantile-comparison plots for variables and for studentized residuals from a linear model. A comparison line is drawn on the plot either through the quartiles of the two distributions, or by robust regression.

Any distribution for which quantile and
density functions exist in R (with prefixes `q`

and `d`

, respectively) may be used.
When plotting a vector, the confidence envelope is based on the SEs of the order statistics
of an independent random sample from the comparison distribution (see Fox, 2016).
Studentized residuals from linear models are plotted against the appropriate t-distribution with a point-wise
confidence envelope computed by default by a parametric bootstrap,
as described by Atkinson (1985).
The function `qqp`

is an abbreviation for `qqPlot`

.

The `envelope`

argument can take a list with the following named elements; if an element is missing, then the default value is used:

`level`

confidence level (default

`0.95`

).`style`

one of

`"filled"`

(the default),`"lines"`

, or`"none"`

.`col`

color (default is the value of

`col.lines`

).`alpha`

transparency/opacity of a filled confidence envelope, a number between 0 and 1 (default

`0.15`

).`border`

controls whether a border is drawn around a filled confidence envelope (default

`TRUE`

).

Fox, J. (2016)
*Applied Regression Analysis and Generalized Linear Models*,
Third Edition. Sage.

Fox, J. and Weisberg, S. (2019)
*An R Companion to Applied Regression*, Third Edition, Sage.

Atkinson, A. C. (1985)
*Plots, Transformations, and Regression.* Oxford.

```
x<-rchisq(100, df=2)
qqPlot(x)
qqPlot(x, dist="chisq", df=2, envelope=list(style="lines"))
qqPlot(~ income, data=Prestige, subset = type == "prof")
qqPlot(income ~ type, data=Prestige, layout=c(1, 3))
qqPlot(lm(prestige ~ income + education + type, data=Duncan),
envelope=.99)
```

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