This paper describes a newly proposed empathy prediction model, the EmoCog model, as our solution for the One-Minute Gradual (OMG) Empathy Challenge. The objective for the challenge was to estimate the valence (positivity/negativity) of a listener in a story-telling conversation. We implemented the EmoCog model with two approaches - one with support vector machines (SVMs) and one with neural networks (NNs). We extracted a total of six features corresponding to three categories: 1) cognitive empathy, 2) emotional empathy, 3) synchrony and used them as input to our models. On the validation set, we achieved 0.19 Concordance Correlation Coefficient (CCC) for the SVM approach and 0.25 for the NN approach. On the test set, we achieved results better than baseline, with CCC scores of 0.08 and 0.07, respectively.