This paper presents a two-stage procedure for estimating the parameters and response surface in the general linear model, when different experimental designs are used for the two stages of data collection. A first set of observations is collected according to a known experimental design, and the information from that first sample is used to determine the number of additional observations (collected using the second experimental design) necessary to estimate the parameters or response surface to a predetermined jpoint precision. Asymptotic results are given which depend on the size of the first sample and on the experimental designs.