The heuristic reasoning and experiments based design approach have been the pillars of studies on artificial neural networks. The explainable network performance is required for most applications. We focus on a simple classifier network for the two-class case of AR(1) data sources. We trace the input statistics through the network and quantify changes to explain relationship between accuracy performance, optimized parameters and activation function types employed for the given architecture. We present test accuracy results for various network configurations with different dimension and activation types. AR(1) source model for a two-class case is utilized to generate training and test data sets of the experiments due to its ease of use for analytical study. We quantify the relationships with well known metrics among signal (class) statistics, network architecture, activation function type and accuracy for several correlation coefficient pairs of the two AR(1) sources utilized in this paper. It is observed from the experiments that the analyses of data, input-output relationships of hidden and output layer nodes for the given architecture provide invaluable insights and guidance to judiciously design a neural network and to explain its performance based on characteristics of the building blocks.