There are multiple interpretations for the linear regression coefficients, ci, that result from the linear approximation of an output vector y based on multiple input vectors xi (i = 1 to n). A concise mathematical interpretation for the ci can be obtained by decoupling the input/output system via the techniques of random data analysis. In such case, each ck can be reinterpreted as the correlation coefficient resulting from the linear approximation of the conditioned output for y based solely on the conditioned input for xk. Here, conditioning refers to the removal of the linear contributions of the remaining inputs from both xk and y. In other words, ck is the correlation coefficient resulting from the single input/output system consisting of the residual of xk and the residual of y when the linear contributions of the remaining variables xi (i ≠ k) are eliminated from the system.