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### Abstract

Confirming the precision agriculture hypothesis for variable rate nitrogen applications (VRA) is challenging. To confront this challenge, researchers have used increasingly sophisticated statistical models to estimate and compare site-specific crop response functions (SSCRFs). While progress has been made, it has been hampered by the lack of a conceptual framework to guide the development of appropriate statistical models. This paper provides such a framework and demonstrates its utility by developing a heteroscedastic, fixed and random effects, geostatistical model to test if VRA can increase nitrogen returns. The novelty of the model is the inclusion of site, spatial, treatment, and treatment strip heteroscedasticity and correlation. Applied to data collected in 1995 from two corn nitrogen response experiments in South Central Minnesota, results demonstrate the importance of including site, spatial, treatment, and treatment strip effects in the estimation of SSCRFs. Results also indicate a significant potential for VRA to increase nitrogen returns and that these potential returns increase as the area of the management unit decreases. At one location, there was greater than a 95% chance that VRA could have increased profitability if the cost of implementing VRA was less than 14.5 $ha-1. At the other location, if implementation costs were less than 48.3$ ha-1, there was greater than a 95% chance of increased profitability.