Quantification of human confidence in functional relations

What makes people infer that two continuous-valued entities are functionally related? Involving factors influencing human confidence in the existence of a functional link between two supposed variables has not so far been discussed in function learning literature. By examining this problem and based on relevant results from cognitive psychology, I propose a hypothesis according to which human confidence in a link between cue and criterion is affected by three factors: The difficulty of functions, the level of noise in observed data, and the sample size. Here, the formalization of this hypothesis forms a novel mathematical model of function learning which can also be used for predictions; so the resulting model receives cue-criterion pairs of a supposed relation and produces two outputs: Confidence and predicting function. In an experiment, the performance of a computational implementation of the model is compared with human data. The results show that the model is successful in tracking changes in human confidence. A close correspondence between the predictions of the model and humans was also achieved.