4.6.1.7. Model Fitting

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

4.6.1.7. Model Fitting - Model #2

Based on the residual plots, the function used to describe the data should be the quadratic polynomial:

$D = \beta_0 + \beta_1L + \beta_2L^2$

The computer output from this process is shown below. As for the straight-line 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.

Dataplot Output for Quadratic Fit

LEAST SQUARES POLYNOMIAL FIT
SAMPLE SIZE N       =       40
DEGREE              =        2
REPLICATION CASE
REPLICATION STANDARD DEVIATION =     0.2147264895D-03
REPLICATION DEGREES OF FREEDOM =          20
NUMBER OF DISTINCT SUBSETS     =          20


       PARAMETER ESTIMATES  (APPROX. ST. DEV.)  T VALUE
1  A0     0.673618E-03         (0.1079E-03)       6.2
2  A1     0.732059E-06         (0.1578E-09)     0.46E+04
3  A2    -0.316081E-14         (0.4867E-16)       -65.

RESIDUAL    STANDARD DEVIATION =         0.0002051768
RESIDUAL    DEGREES OF FREEDOM =          37
REPLICATION STANDARD DEVIATION =         0.0002147265
REPLICATION DEGREES OF FREEDOM =          20
LACK OF FIT F RATIO = 0.8107 = THE 33.3818% POINT OF
THE F DISTRIBUTION WITH 17 AND 20 DEGREES OF FREEDOM