Fig. 8

Root mean squared deviation between modeled response and observed values for different transformation parameters. Deviation was measured by \(\text {avg}((\bar {\hat {y}} - y)^{2})\). Here, the back-transformed estimate was defined by \( \hat{y}=\left[ JWFFXGRAPHICS\right]s12874-021-01356-0\mathrm{flba}.\mathrm{eps}{\left[ JWFFXGRAPHICS\right]}^{-1}\left({\hat{y}}^{\left(\lambda \right)}+\hat{\varepsilon}\right) \) (if [JWFFXGRAPHICS]s12874−021−01356−0flbb.eps[JWFFXGRAPHICS]⁻¹ existed), where [JWFFXGRAPHICS]s12874−021−01356−0flbc.eps[JWFFXGRAPHICS]⁻¹ was the inverse Box-Cox transformation, and \(\bar {\hat {y}}\) was its mean (computed from sampling 10,000 times from the fitted residuals). For λ=0.45, the deviation was 1.10mm² and a minimal squared deviation was reached at λ=0.55 with a deviation of 1.05mm²