\HeaderA{mlbench.friedman3}{Benchmark Problem Friedman 3}{mlbench.friedman3}
\keyword{datagen}{mlbench.friedman3}
\begin{Description}\relax
The regression problem Friedman 3 as described in Friedman (1991) and
Breiman (1996). Inputs are 4 independent variables uniformly
distrtibuted over the ranges
\deqn{0 \le x1 \le 100}{}
\deqn{40 \pi \le x2 \le 560 \pi}{}
\deqn{0 \le x3 \le 1}{}
\deqn{1 \le x4 \le 11}{}

The outputs are created according to the formula
\deqn{y = \mbox{atan}((x2 x3 - (1/(x2 x4)))/x1) + e}{y = atan ((x2 x3 - (1/(x2 x4)))/x1) + e}

where e is N(0,sd).
\end{Description}
\begin{Usage}
\begin{verbatim}
mlbench.friedman3(n, sd=0.1)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{n}] number of patterns to create
\item[\code{sd}] Standard deviation of noise. The default value of 0.1 gives
a signal to noise ratio (i.e., the ratio of the standard deviations) of
3:1. Thus, the variance of the function itself (without noise)
accounts for 90\% of the total variance.
\end{ldescription}
\end{Arguments}
\begin{Value}
Returns a list with components
\begin{ldescription}
\item[\code{x}] input values (independent variables)
\item[\code{y}] output values (dependent variable)
\end{ldescription}
\end{Value}
\begin{References}\relax
Breiman, Leo (1996) Bagging predictors. Machine Learning 24, pages
123-140.

Friedman, Jerome H. (1991) Multivariate adaptive regression
splines. The Annals of Statistics 19 (1), pages 1-67.
\end{References}

