The Coefficient of Importance (CoI) was developed to quantify the input variable importance by using the CoD measure. Based on a polynomial model, including all investigated variables, the CoI of a single variable Xi with respect to the response Y is defined as follows

(2–13)

where is the CoD of the full model including all terms of the variables in X and is the CoD of the reduced model, where all linear, quadratic and interactions terms belonging to X_i are removed from the polynomial basis. For both cases the same set of sampling points is used. If a variable has low importance, its CoI is close to zero, since the full and the reduced polynomial regression model have a similar quality. The CoI is equivalent to the explained variation with respect to a single input variable, since the CoD quantifies the explained variation of the polynomial approximation. Thus it is an estimate of the total effect sensitivity measure given in Equation 2–3. If the polynomial model contains important interaction terms, the sum of the CoI values should be larger than the CoD of the full model.

Since it is based on the CoD, the CoI is also limited to polynomial models. If the total explained variation is over-estimated by the CoD, the CoI may also give a wrong estimate of the variance contribution of the single variables. However, in contrast to the Coefficient of Correlation, the CoI can handle linear and quadratic dependencies including input variable interactions. Furthermore, an assessment of the suitability of the polynomial basis is possible. Nevertheless, an estimate of the CoI values using a full quadratic polynomial is often not possible because of the required large number of samples for high dimensional problems.