A data.frame with numeric response and real overall mean and three predictors generated from truncated multivariate normal distribution.
Details
The three predictors generated from truncated multivariate normal distribution \(TN(0, \Sigma, -2, 2)\) , with mean zero and covariance matrix \(\Sigma=(0.3^{\mathbb{1}(i \ne j)})\) , and each predictor lies in \([-2, 2]\).
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 rtmvnorm function in package TruncatedNormal.