Precision Agriculture has been gaining interest due to the significant growth in the fields of engineering and computer science, hence leading to more sophisticated methods and tools to improve agricultural techniques. One approach to Precision Agriculture involves the application of mathematical models and machine learning to fertilization optimization and yield prediction, which is what this research focuses on. Specifically, in this work we report the results of predicting yield and protein content of winter wheat over four farms based on the levels of nitrogen fertilizer applied to the fields. The intent is to use these predictions as a basis for prescribing fertilizer application to optimize net returns on the subsequent harvest. More specifically, we compare methods based on multiple regression (linear and non-linear) and neural networks (shallow and deep). Our results indicate that a deep neural network based on the stacked autoencoder that includes spatial sampling yields the best results.