# ns

##### Generate a Basis Matrix for Natural Cubic Splines

Generate the B-spline basis matrix for a natural cubic spline.

- Keywords
- smooth

##### Usage

```
ns(x, df = NULL, knots = NULL, intercept = FALSE,
Boundary.knots = range(x))
```

##### Arguments

- x
the predictor variable. Missing values are allowed.

- df
degrees of freedom. One can supply

`df`

rather than knots;`ns()`

then chooses`df - 1 - intercept`

knots at suitably chosen quantiles of`x`

(which will ignore missing values). The default,`df = NULL`

, sets the number of inner knots as`length(knots)`

.- knots
breakpoints that define the spline. The default is no knots; together with the natural boundary conditions this results in a basis for linear regression on

`x`

. Typical values are the mean or median for one knot, quantiles for more knots. See also`Boundary.knots`

.- intercept
if

`TRUE`

, an intercept is included in the basis; default is`FALSE`

.- Boundary.knots
boundary points at which to impose the natural boundary conditions and anchor the B-spline basis (default the range of the data). If both

`knots`

and`Boundary.knots`

are supplied, the basis parameters do not depend on`x`

. Data can extend beyond`Boundary.knots`

##### Details

`ns`

is based on the function `splineDesign`

. It
generates a basis matrix for representing the family of
piecewise-cubic splines with the specified sequence of
interior knots, and the natural boundary conditions. These enforce
the constraint that the function is linear beyond the boundary knots,
which can either be supplied or default to the extremes of the
data.

A primary use is in modeling formula to directly specify a natural spline term in a model: see the examples.

##### Value

A matrix of dimension `length(x) * df`

where either `df`

was
supplied or if `knots`

were supplied,
`df = length(knots) + 1 + intercept`

.
Attributes are returned that correspond to the arguments to `ns`

,
and explicitly give the `knots`

, `Boundary.knots`

etc for
use by `predict.ns()`

.

##### References

Hastie, T. J. (1992)
Generalized additive models.
Chapter 7 of *Statistical Models in S*
eds J. M. Chambers and T. J. Hastie, Wadsworth & Brooks/Cole.

##### See Also

##### Examples

`library(splines)`

```
# NOT RUN {
require(stats); require(graphics)
ns(women$height, df = 5)
summary(fm1 <- lm(weight ~ ns(height, df = 5), data = women))
## To see what knots were selected
attr(terms(fm1), "predvars")
## example of safe prediction
plot(women, xlab = "Height (in)", ylab = "Weight (lb)")
ht <- seq(57, 73, length.out = 200) ; nD <- data.frame(height = ht)
lines(ht, p1 <- predict(fm1, nD))
stopifnot(all.equal(p1, predict(update(fm1, . ~
splines::ns(height, df=5)), nD)))
# not true in R < 3.5.0
# }
```

*Documentation reproduced from package splines, version 3.6.2, License: Part of R 3.6.2*