Crelated

Crelated is a theoretical metric in statistics and data analysis used to quantify the extent to which a variable is related to a specified set of covariates, denoted C. The concept sits as a generalization of correlation by conditioning on C and measuring the remaining association with a target variable. Operationally, Crelated can be defined as the correlation between the residuals of a primary variable and the residuals of a target variable after regressing each on the covariate set C. In that sense, it parallels partial correlation, which removes linear effects of C.

Usage and computation: In practice, one fits regression models to X and Y on C, obtains residuals X_res and Y_res, and computes their Pearson correlation. For non-linear relationships, residuals can be derived from flexible models or via rank-based methods, and the correlation can be computed on those residuals. Crelated can thus reflect direct associations after accounting for C.

Properties and limitations: The value of Crelated depends on model specification and sample size; it is most reliable when C captures the principal confounding structure. Like partial correlation, it ranges roughly between -1 and 1 under linear assumptions, but interpretation can be sensitive to nonlinearity and outliers. Robust or bootstrap methods can improve stability.

Relation and alternatives: Crelated is related to partial correlation, semi-partial correlation, and conditional correlation, and is distinct from mutual information or distance correlation, which assess broader dependencies.

Applications: Used in feature selection, causal inference, genomics, and economics to assess direct associations while controlling for confounders.

Etymology: A blend of the use of covariates denoted C and the idea of “relatedness.”