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

4.6.1.3.

Model Fitting - Initial Model

Least Squares Estimation

Using software for computing least squares parameter estimates, the straight-line model, $$ D = \beta_0 + \beta_1L + \varepsilon \, ,$$ is easily fit to the data. The regression results are shown below. Before trying to interpret all of the numerical output, however, it is critical to check that the assumptions underlying the parameter estimation are met reasonably well. The next two sections show how the underlying assumptions about the data and model are checked using graphical and numerical methods.

Regression Results

Parameter       Estimate    Stan. Dev    t Value
B0          0.614969E-02   0.7132E-03        8.6
B1          0.722103E-06   0.3969E-09   0.18E+04

Residual standard deviation = 0.0021712694
Residual degrees of freedom = 38

Lack-of-fit F statistic              = 214.7464 
Lack-of-fit critical value, F0.05,18,20 = 2.15