Choosing Box‑Cox vs Manual Log‑Plus‑Constant for Right‑Skewed Responses with Zeros in Minitab Regression

The task is to transform a right‑skewed response that contains zeros for regression analysis in Minitab, using a documented feature.

Box‑Cox automatic lambda estimation requires strictly positive values, so the presence of zeros prevents the transformation from being applied, while the manual log‑plus‑constant method adds a chosen constant to zeros before logging, giving explicit control but no guidance on selecting that constant.

What criterion should an analyst use to select the constant added before logging when zeros are present? Does Minitab provide any documented rule for constant selection in the log‑plus‑constant method? Which transformation preserves model diagnostics consistency across versions?