4.
Process Modeling
4.6. Case Studies in Process Modeling 4.6.1. Load Cell Calibration


New Function  Based on the residual plots, the function used to describe the data should be the quadratic polynomial, $$ D = \beta_0 + \beta_1L + \beta_2L^2 + \varepsilon \, . $$ The regression results are shown below. As for the straightline model, however, it is important to check that the assumptions underlying the parameter estimation are met before trying to interpret the numerical output. The steps used to complete the graphical residual analysis are essentially identical to those used for the previous model.  
Quadratic Fit 
Parameter Estimate Stan. Dev t Value B0 0.673618E03 0.1079E03 6.2 B1 0.732059E06 0.1578E09 0.46E+04 B2 0.316081E14 0.4867E16 65.0 Residual standard deviation = 0.0002051768 Residual degrees of freedom = 37 Lackoffit F statistic = 0.8107 Lackoffit critical value, F_{0.05,17,20} = 2.17 