A case study of regression analysis based on modeling Gilliland's correlation was described for use in a computational methods course. The case study uses a familiar example to train students in nonlinear least squares regression and to use standardized residual plots for model assessment. Previously published equations for Gilliland's correlation were reviewed improved by refitting Gilliland's data using nonlinear least squares regression. A new two-parameter rational equation was found to be superior to previously reported Gilliland equations as the only model that meets all the theoretical end conditions without compromise. The new and improved equation for Gilliland's correlation is recommended for preliminary shortcut methods of distillation column design and analysis.