# plot.lm

0th

Percentile

##### Plot Diagnostics for an lm Object

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.

Keywords
hplot, regression
##### Usage
## S3 method for class 'lm':
plot(x, which = c(1:3, 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) panel.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),
cex.caption = 1, cex.oma.main = 1.25)
##### Arguments
x
lm object, typically result of lm or glm.
which
if a subset of the plots is required, specify a subset of the numbers 1:6.
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$call) is used. main title to each plot---in addition to caption. ask logical; if TRUE, the user is asked before each plot, see par(ask=.). ... other parameters to be passed through to plotting functions. id.n number of points to be labelled in each plot, starting with the most extreme. labels.id vector of labels, from which the labels for extreme points will be chosen. NULL uses observation numbers. cex.id magnification of point labels. qqline logical indicating if a qqline() should be added to the normal Q-Q plot. cook.levels levels of Cook's distance at which to draw contours. add.smooth logical indicating if a smoother should be added to most plots; see also panel above. label.pos positioning of labels, for the left half and right half of the graph respectively, for plots 1-3. cex.caption controls the size of caption. cex.oma.main controls the size of the sub.caption only if that is above the figures when there is more than one. ##### Details sub.caption---by default the function call---is shown as a subtitle (under the x-axis title) on each plot when plots are on separate pages, or as a subtitle in the outer margin (if any) when there are multiple plots per page. The Scale-Location plot, also called Spread-Location or S-L plot, takes the square root of the absolute residuals in order to diminish skewness ($\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 that are equal in magnitude are lines through the origin. The contour lines are labelled with the magnitudes.

##### References

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.

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