Understanding the relationships between yield and soil properties and topographic characteristics is of critical importance in precision agriculture. A necessary first step is to identify techniques to reliably quantify the relationships between soil and topographic characteristics and crop yield. Stepwise multiple linear regression (SMLR), projection pursuit regression (PPR), and several types of supervised feed–forward neural networks were investigated in an attempt to identify methods able to relate soil properties and grain yields on a point–by–point basis within ten individual site–years. To avoid overfitting, evaluations were based on predictive ability using a 5–fold cross–validation technique. The neural techniques consistently outperformed both SMLR and PPR and provided minimal prediction errors in every site–year. However, in site–years with relatively fewer observations and in site–years where a single, overriding factor was not apparent, the improvements achieved by neural networks over both SMLR and PPR were small. A second phase of the experiment involved estimation of crop yield across multiple site–years by including climatological data. The ten site–years of data were appended with climatological variables, and prediction errors were computed. The results showed that significant overfitting had occurred and indicated that a much larger number of climatologically unique site–years would be required in this type of analysis.