This data collection is associated with the article ``I See What You Did There'': Understanding People's Social Perception of a Robot and its Predictability, published in ACM Transactions in Human-Robot Interaction in 2021. Abstract:Unpredictability in robot behaviour can cause difficulties in interacting with robots. However, for social interactions with robots, a degree of unpredictability in robot behaviour may be desirable for facilitating engagement and increasing the attribution of mental states to the robot. To generate a better conceptual understanding of predictability, we looked at two facets of predictability, namely the ability to predict robot actions and the association of predictability as an attribute of the robot. We carried out a video human-robot interaction study where we manipulated whether participants could either see the cause of a robot's responsive action, or could not see this, because there was no cause, or because we obstructed the visual cues. Our results indicate that when the cause of the robot's responsive actions was not visible, participants rated the robot as more unpredictable and less competent, compared to when it was visible. The relationship between seeing the cause of the responsive actions and the attribution of competence was partially mediated by the attribution of unpredictability to the robot. We argue that the effects of unpredictability may be mitigated when the robot identifies when a person may not be aware of what the robot wants to respond to, and uses additional actions to make its response predictable.