4.6.1.3. Model Fitting - Initial Model

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,

is easily fit to the data. The computer output from this process is 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.

Dataplot Output

LEAST SQUARES POLYNOMIAL FIT
SAMPLE SIZE N       =       40
DEGREE              =        1
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     0.614969E-02          (0.7132E-03)        8.6
2 A1     0.722103E-06          (0.3969E-09)      0.18E+04

RESIDUAL    STANDARD DEVIATION =         0.0021712694
RESIDUAL    DEGREES OF FREEDOM =          38
REPLICATION STANDARD DEVIATION =         0.0002147265
REPLICATION DEGREES OF FREEDOM =          20
LACK OF FIT F RATIO = 214.7464 = THE 100.0000% POINT OF
THE F DISTRIBUTION WITH 18 AND  20 DEGREES OF FREEDOM