Summary: This paper is concerned with Bayes prediction in a linear regression model when the density of the observations is given by \[ f(y|\beta,\tau^2)=\int_{z>0} (2\pi)^{-n/2} (\tau^2)^{n/2} \{\psi (z)^{-2}\}^{n/2}\times \exp \left(-\frac{\tau^2}2\psi(z)^{-2} \|y-X\beta\|^2\right) dG(z), \] where \(y\in\mathbb{R}^n\), \(\beta\in\mathbb{R}^k\), \(\tau^2>0\), \(Z\) is a positive random variable with distribution function \(G\), \(\psi(\cdot)\) is a positive function, and \(\|\;\|\) denotes the Euclidean norm. We show that when prior information is objective or in the conjugate family, the Bayes prediction density is the same as that when the density of the observations is normal, for any \(Z\).