You are interesting in fitting aneural network for a regression problem by minimizing the sum of squared errors.$($SSE$)$ You wil use backpropagation to calculate the derivatives as part of the optimization algorithim. The squared residual of the n$-$th data point is Rn$,$ the neural network response for the n$-$th data point is fn$.$ The residual or error of the n$-$th data point is