We demonstrate the special condition where the Q-learning and regression models provide an identical prediction. This is the case when the following three conditions hold: (1) the forgetting and learning rates are identical (αL = αF ; F-Q model), (2) the influence of the initial action value can be neglected (e.g., the initial values are zero), and (3) the cutoff effect of the history length (Mr ) included in the regression model can be neglected. When the first condition is not met (i.e., when the forgetting rate differs from the learning rate), as is the case for the standard Q-learning model (αF = 0), a dependence on choice history arises. This dependence on choice history is relatively complex and cannot be completely captured by a conventional regression model. This dependence on choice history is a property of the RL model, which distinguishes it from simple regression models. It should be noted that this apparent dependence on choice history was found only by examining the relationship between regression models and RL models, as we have done in the present study, rather than by simply examining the RL model itself.