# line

##### Robust Line Fitting

Fit a line robustly as recommended in *Exploratory Data Analysis*.

Currently the initial median-median line is *not* iterated (as
opposed to Tukey's “resistant line” in the references).

- Keywords
- robust, regression

##### Usage

`line(x, y, iter = 1)`

##### Arguments

- x, y
the arguments can be any way of specifying x-y pairs. See

`xy.coords`

.- iter
positive integer specifying the number of “polishing” iterations. Note that this was hard coded to

`1`

in R versions before 3.5.0, and more importantly that such simple iterations may not converge, see Siegel's 9-point example.

##### Details

Cases with missing values are omitted.

Contrary to the references where the data is split in three (almost)
equally sized groups with symmetric sizes depending on \(n\) and
`n %% 3`

and computes medians inside each group, the
`line()`

code splits into three groups using all observations
with `x[.] <= q1`

and `x[.] >= q2`

, where `q1, q2`

are
(a kind of) quantiles for probabilities \(p = 1/3\) and \(p = 2/3\)
of the form `(x[j1]+x[j2])/2`

where `j1 = floor(p*(n-1))`

and `j2 = ceiling(p(n-1))`

, `n = length(x)`

.

Long vectors are not supported yet.

##### Value

An object of class `"tukeyline"`

.

Methods are available for the generic functions `coef`

,
`residuals`

, `fitted`

, and `print`

.

##### References

Tukey, J. W. (1977).
*Exploratory Data Analysis*,
Reading Massachusetts: Addison-Wesley.

Velleman, P. F. and Hoaglin, D. C. (1981).
*Applications, Basics and Computing of Exploratory Data Analysis*,
Duxbury Press.
Chapter 5.

Emerson, J. D. and Hoaglin, D. C. (1983).
Resistant Lines for \(y\) versus \(x\).
Chapter 5 of *Understanding Robust and Exploratory Data Analysis*,
eds. David C. Hoaglin, Frederick Mosteller and John W. Tukey. Wiley.

Iain M. Johnstone and Paul F. Velleman (1985).
The Resistant Line and Related Regression Methods.
*Journal of the American Statistical Association*, **80**,
1041--1054.
10.2307/2288572.

##### See Also

`lm`

.

There are alternatives for robust linear regression more robust and
more (statistically) efficient,
see `rlm()`

from MASS, or
`lmrob()`

from robustbase.

##### Examples

`library(stats)`

```
# NOT RUN {
require(graphics)
plot(cars)
(z <- line(cars))
abline(coef(z))
## Tukey-Anscombe Plot :
plot(residuals(z) ~ fitted(z), main = deparse(z$call))
## Andrew Siegel's pathological 9-point data, y-values multiplied by 3:
d.AS <- data.frame(x = c(-4:3, 12), y = 3*c(rep(0,6), -5, 5, 1))
cAS <- with(d.AS, t(sapply(1:10,
function(it) line(x,y, iter=it)$coefficients)))
dimnames(cAS) <- list(paste("it =", format(1:10)), c("intercept", "slope"))
cAS
## iterations started to oscillate, repeating iteration 7,8 indefinitely
# }
```

*Documentation reproduced from package stats, version 3.5.0, License: Part of R 3.5.0*