\HeaderA{mlbench.friedman1}{Benchmark Problem Friedman 1}{mlbench.friedman1}
\keyword{datagen}{mlbench.friedman1}
\begin{Description}\relax
The regression problem Friedman 1 as described in Friedman (1991) and
Breiman (1996). Inputs are 10 independent variables uniformly
distributed on the interval \eqn{[0,1]}{}, only 5 out of these 10 are actually
used. Outputs are created according to
the formula
\deqn{y = 10 \sin(\pi x1 x2) + 20 (x3 - 0.5)^2 + 10 x4 + 5 x5 + e}{y = 10 sin(\pi x1 x2) + 20 (x3 - 0.5)^2
+ 10 x4 + 5 x5 + e}

where e is N(0,sd).
\end{Description}
\begin{Usage}
\begin{verbatim}
mlbench.friedman1(n, sd=1)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{n}] number of patterns to create
\item[\code{sd}] Standard deviation of noise
\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}

