# Generate a Basis Matrix for Natural Cubic Splines

### Description

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

### Usage

1 2 |

### Arguments

`x` |
the predictor variable. Missing values are allowed. |

`df` |
degrees of freedom. One can supply |

`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 |

`intercept` |
if |

`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 |

### Details

`ns`

is based on the function `spline.des`

. 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

`bs`

, `predict.ns`

, `SafePrediction`

### Examples

1 2 3 4 5 6 7 8 9 10 11 | ```
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)
lines(ht, predict(fm1, data.frame(height = ht)))
``` |