In a wide range of natural phenomena and engineering processes, physical experimentation is resource-intensive or even impossible, motivating the now widespread use of mathematical models implemented as computer codes. This complementary way of doing science has for decades spawned corresponding research in statistical methodologies for the careful design and analysis of computer experiments (DACE, Currin et al., 1991; Sacks et al., 1989). When a complex computer code is expensive to evaluate, DACE replaces the code by a fast statistical model surrogate trained with limited code runs. The surrogate most commonly employed treats the unknown input-output function as a realization of a Gaussian stochastic process (GaSP), also known simply as a Gaussian process (GP). While there are many possible objectives of such an experiment, e.g., optimization or calibration, prediction of the original computer code output by the statistical surrogate underlies tackling the scientific objective. Therefore, obtaining good accuracy at untried values of the input variables is a fundamental goal. Typically, input variables are in a "raw" form, as provided to the code, and the output is similarly as produced by the code or some summary. This article maintains the basic GaSP surrogate paradigm but proposes to improve prediction accuracy by input and output transformations guided by dimensional analysis (DA), which is related to physical units of measurement (and not the number of variables).