The advance of Ubiquitous Computing (UbiComp) and Internet of Things (IoT) brought a new set of Non-Functional Requirements (NFRs), especially related to Human-Computer Interaction (HCI). Invisibility is one of these NFRs and refers to either the merging of technology in the user environment or the decrease in the interaction workload. This new NFR may impact traditional ones (e.g., Usability), revealing positive correlations, when one NFR helps another, and negative correlations, when a procedure favors an NFR but creates difficulty for another one. Correlations between NFRs are usually stored in catalogs, which is a well-defined body of knowledge gathered from previous experience. Although Invisibility has been recently cataloged with development strategies, the literature still lacks catalogs with correlations for this NFR. Therefore, this work aims at capturing and cataloging invisibility correlations for UbiComp and IoT systems. To do that, we also propose to systematize the definition of correlations using the following well-defined research methods: Interview, Content Analysis and Questionnaire. As a result, we defined a catalog with 110 positive and negative correlations with 9 NFRs. We evaluated this correlation catalog using a controlled experiment to verify if it helps developers when they are making decisions about NFRs in UbiComp and IoT systems. Results indicated that the catalog improved the decisions made by the participants. Therefore, this well-defined body of knowledge is useful for supporting software engineers to select appropriate strategies that satisfy Invisibility and other NFRs related to user interaction.