# qqPlot

##### Quantile-Comparison Plots

Plots empirical quantiles of a variable, or of studentized residuals from a linear model, against theoretical quantiles of a comparison distribution.

- Keywords
- distribution, regression, univar

##### Usage

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

# S3 method for default
qqPlot(x, distribution="norm", ...,
ylab=deparse(substitute(x)), xlab=paste(distribution, "quantiles"),
main=NULL, las=par("las"),
envelope=.95,
col=palette()[1], col.lines=palette()[2], lwd=2, pch=1, cex=par("cex"),
line=c("quartiles", "robust", "none"),
labels = if(!is.null(names(x))) names(x) else seq(along=x),
id.method = "y",
id.n =if(id.method[1]=="identify") Inf else 0,
id.cex=1, id.col=palette()[1], id.location="lr", grid=TRUE)

# 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=.95,
reps=100, col=palette()[1], col.lines=palette()[2], lwd=2,
pch=1, cex=par("cex"),
labels, id.method = "y",
id.n = if(id.method[1]=="identify") Inf else 0,
id.cex=1, id.col=palette()[1], id.location="lr", grid=TRUE, ...)

##### Arguments

- 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.- ylab
label for vertical (empirical quantiles) axis.

- xlab
label for horizontal (comparison quantiles) axis.

- main
label for plot.

- envelope
confidence level for point-wise confidence envelope, or

`FALSE`

for no envelope.- 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 color palette (see`palette`

and`par`

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

*second*entry in the current color 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`

.- labels
vector of text strings to be used to identify points, defaults to

`names(x)`

or observation numbers if`names(x)`

is`NULL`

.- id.method
point identification method. The default

`id.method="y"`

will identify the`id.n`

points with the largest value of`abs(y-mean(y))`

. See`showLabels`

for other options.- id.n
number of points labeled. If

`id.n=0`

, the default, no point identification.- id.cex
set size of the text for point labels; the default is

`cex`

(which is typically`1`

).- id.col
color for the point labels.

- id.location
The default

`"lr"`

identifies to the left or right of the point; the alterative`"ab"`

identifies above or below the point.- 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

##### Details

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, 2008).
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`

.

##### Value

These functions return the labels of identified points.

##### References

Fox, J. (2008)
*Applied Regression Analysis and Generalized Linear Models*,
Second Edition. Sage.

Fox, J. and Weisberg, S. (2011)
*An R Companion to Applied Regression*, Second Edition, Sage.

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

##### See Also

##### Examples

```
# NOT RUN {
x<-rchisq(100, df=2)
qqPlot(x)
qqPlot(x, dist="chisq", df=2)
qqPlot(lm(prestige ~ income + education + type, data=Duncan),
envelope=.99)
# }
```

*Documentation reproduced from package car, version 2.1-6, License: GPL (>= 2)*