The Rational Inattention (RI) model has attracted attention in recent years as a promising candidate for modeling bounded rationality in the fields of decision making and game theory research. The model assumes that there is a cognitive cost (cost of information processing) that is proportional to the amount of mutual information obtained from signals, thereby making it possible to explain various phenomena observed in the market at a certain level. However, the RI model still lacks a sufficient cognitive foundation. In this study, we conducted an experiment to examine whether the cognitive costs and constraints on information processing, which are the assumptions of the Rational Inattention Model, are reasonable from the perspective of neuroeconomics using biometric data such as gaze information and brain responses. We adopted the sequential investment task with a view to applying it to finance. Our results showed that the stochastic choice rational inattention model fit the behavioral data of the present experiment, the larger the cognitive cost the more activated the brain regions involved in costly cognition, And the consistency between gaze information and the capacity constraint of the Kalman filter type model, as expected, when there is a lot of information, not all information can be processed, so more accurate decisions cannot be made.