Figure 2.

Illustration of the combined classical and inverse N-way HC-PLSR metamodelling. The inverse metamodelling was carried out first, defining the clusters to use also in the classical metamodelling. The classification of the test set observations to be predicted in the classical metamodelling was based on ${\widehat{\mathit{T}}}_{\text{OutputA,Inverse}}$, predicted from ${\widehat{\mathit{T}}}_{\text{YA,NWay}}$(see Additional file 1, eq. S12c for a definition) using second order polynomial Ordinary Least Squares (OLS) regression (called function $\widehat{F}$(.)). See Additional file 1 sections S1.5-S1.7 for a more comprehensive description of this methodology, including predicting equations for test set observations. *See Additional file 1, equation S9b. ^**C_A and C2_A were calculated by equation S12b in Additional file 1.