The regression problem Friedman 3 as described in Friedman (1991) and Breiman (1996). Inputs are 4 independent variables uniformly distrtibuted over the ranges $$0 \le x1 \le 100$$ $$40 \pi \le x2 \le 560 \pi$$ $$0 \le x3 \le 1$$ $$1 \le x4 \le 11$$
The outputs are created according to the formula $$y = \mbox{atan}((x2 x3 - (1/(x2 x4)))/x1) + e$$
where e is N(0,sd).
mlbench.friedman3(n, sd=0.1)number of patterns to create
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.
Returns a list with components
input values (independent variables)
output values (dependent variable)
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.