A cDNA microarray is a complex biochemical-optical system whose purpose is the simultaneous measurement of gene expression for thousands of genes. In this paper we propose a general statistical approach to finding associations between the expression patterns of genes via the coefficient of determination. This coefficient measures the degree to which the transcriptional levels of an observed gene set can be used to improve the prediction of the transcriptional state of a target gene relative to the best possible prediction in the absence of observations. The method allows incorporation of knowledge of other conditions relevant to the prediction, such as the application of particular stimuli or the presence of inactivating gene mutations, as predictive elements affecting the expression level of a given gene. Various aspects of the method are discussed: prediction quantification, unconstrained prediction, constrained prediction using ternary perceptrons, and design of predictors given small numbers of replicated microarrays. The method is applied to a set of genes undergoing genotoxic stress for validation according to the manner in which it points toward previously known and unknown relationships. The entire procedure is supported by software that can be applied to large gene sets, has a number of facilities to simplify data analysis, and provides graphics for visualizing experimental data, multiple gene interaction, and prediction logic.