Is that a definition of correlation inside the field of mathematics? Because the normal English definition of correlation just means a connection, and absolutely doesn't mean linear.
edit: Ah, Wikipedia intro suggests that yes it's specific within statistics (though still seems to not be a hard requirement to call something a correlation?): "In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it normally refers to the degree to which a pair of variables are linearly related." https://en.wikipedia.org/wiki/Correlation
"a connection or relationship between two or more facts, numbers, etc." https://dictionary.cambridge.org/dictionary/english/correlat...
edit: Ah, Wikipedia intro suggests that yes it's specific within statistics (though still seems to not be a hard requirement to call something a correlation?): "In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it normally refers to the degree to which a pair of variables are linearly related." https://en.wikipedia.org/wiki/Correlation