Simulated Regression Problem Friedman 3

The regression problem Friedman 3 as described in Friedman (1991) and Breiman (1996). Inputs are 4 independent variables uniformly distributed 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 $$\mbox{atan}((x2 x3 - (1/(x2 x4)))/x1) + e$$ where e is \(N(0,sd^2)\).

Usage

sim.Friedman3(n, sd=0.1)

Arguments

n

number of data points to create

sd

Standard deviation of noise. The default value of 125 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.

Value

Returns a list with components

x

input values (independent variables)

y

output values (dependent variable)

References

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.

See also

Other bark deprecated functions: bark-deprecated, bark-package-deprecated, sim.Circle-deprecated, sim.Friedman1-deprecated, sim.Friedman2-deprecated

Examples

if (FALSE) { # \dontrun{
sim.Friedman3(n=100, sd=0.1)
} # }