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% File src/library/splines/man/ns.Rd
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% File src/library/splines/man/ns.Rd
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% Part of the R package, http://www.R-project.org
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% Part of the R package, http://www.R-project.org
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% Copyright 1995-2012 R Core Team
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% Copyright 1995-2013 R Core Team
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% Distributed under GPL 2 or later
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% Distributed under GPL 2 or later
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\name{ns}
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\name{ns}
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\alias{ns}
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\alias{ns}
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\title{Generate a Basis Matrix for Natural Cubic Splines}
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\title{Generate a Basis Matrix for Natural Cubic Splines}
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    boundary conditions and anchor the B-spline basis (default the range
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    boundary conditions and anchor the B-spline basis (default the range
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    of the data).  If both \code{knots} and \code{Boundary.knots} are
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    of the data).  If both \code{knots} and \code{Boundary.knots} are
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    supplied, the basis parameters do not depend on \code{x}. Data can
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    supplied, the basis parameters do not depend on \code{x}. Data can
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    extend beyond \code{Boundary.knots}}
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    extend beyond \code{Boundary.knots}}
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}
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}
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\value{
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\details{
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    A matrix of dimension \code{length(x) * df} where either \code{df} was
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  \code{ns} is based on the function \code{\link{spline.des}}.  It
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    supplied or if \code{knots} were supplied,
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  generates a basis matrix for representing the family of
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    \code{df = length(knots) + 1 + intercept}.
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  piecewise-cubic splines with the specified sequence of
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    Attributes are returned that correspond to the arguments to \code{ns},
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  interior knots, and the natural boundary conditions.  These enforce
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    and explicitly give the \code{knots}, \code{Boundary.knots} etc for
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  the constraint that the function is linear beyond the boundary knots,
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    use by \code{predict.ns()}.
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  which can either be supplied or default to the extremes of the
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  data.
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    \code{ns()} is based on the function \code{\link{spline.des}}.  It
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  A primary use is in modeling formula to directly specify a
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    generates a basis matrix for representing the family of
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  natural spline term in a model: see the examples.
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}
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\value{
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    piecewise-cubic splines with the specified sequence of
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  A matrix of dimension \code{length(x) * df} where either \code{df} was
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    interior knots, and the natural boundary conditions.  These enforce
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  supplied or if \code{knots} were supplied,
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    the constraint that the function is linear beyond the boundary knots,
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  \code{df = length(knots) + 1 + intercept}.
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    which can either be supplied, else default to the extremes of the
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  Attributes are returned that correspond to the arguments to \code{ns},
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    data.  A primary use is in modeling formula to directly specify a
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  and explicitly give the \code{knots}, \code{Boundary.knots} etc for
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    natural spline term in a model.
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  use by \code{predict.ns()}.
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}
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}
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\seealso{
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\seealso{
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  \code{\link{bs}}, \code{\link{predict.ns}}, \code{\link{SafePrediction}}
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  \code{\link{bs}}, \code{\link{predict.ns}}, \code{\link{SafePrediction}}
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}
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}
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\references{
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\references{
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\examples{
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\examples{
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require(stats); require(graphics)
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require(stats); require(graphics)
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ns(women$height, df = 5)
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ns(women$height, df = 5)
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summary(fm1 <- lm(weight ~ ns(height, df = 5), data = women))
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summary(fm1 <- lm(weight ~ ns(height, df = 5), data = women))
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## To see what knots were selected
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attr(terms(fm1), "predvars")
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## example of safe prediction
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## example of safe prediction
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plot(women, xlab = "Height (in)", ylab = "Weight (lb)")
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plot(women, xlab = "Height (in)", ylab = "Weight (lb)")
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ht <- seq(57, 73, length.out = 200)
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ht <- seq(57, 73, length.out = 200)
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lines(ht, predict(fm1, data.frame(height = ht)))
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lines(ht, predict(fm1, data.frame(height = ht)))
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\dontshow{
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\dontshow{