A data.frame with numeric response and real overall mean and three predictors generated from truncated multivariate exponential distribution.
Details
The three predictors generated from truncated multivariate exponential distribution with covariance matrix \(\Sigma=(0.3^{\mathbb{1}(i \ne j)})\). The marginal distribution is exponential distribution with rate 1, and is truncated by 4 and translated to \([-2, 2]\).
The response are generated by \(y = m(x) + \epsilon\), where $$\begin{aligned} m(x) &= m_1(x_1) + m_2(x_2) + m_3(x_3) \\ &= \frac{8}{4 + x_1} + \frac{\exp(3-x^2_2)}{4} + 1.5\sin(\frac{\pi}{2}x_3), \end{aligned}$$ and \(\epsilon\) follows \(N(0, \sigma^2)\), the variance is \(\sigma^2=0.25\).
We generated the above predictors using the ellipCopula and rCopula function in package copula.