4.6.1.5. Interpretation of Numerical Output

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

4.6.1.5. Interpretation of Numerical Output - Initial Model

Lack-of-Fit Statistic Interpretable

The fact that the residual plots clearly indicate a problem with the specification of the function describing the systematic variation in the data means that there is little point in looking at most of the numerical results from the fit. However, since there are replicate measurements in the data, the lack-of-fit test can also be used as part of the model validation. The numerical results of the fit from Dataplot are list below.

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

Function Incorrect

The lack-of-fit test statistic is 214.7534, which also clearly indicates that the functional part of the model is not right. The 95% cut-off point for the test is 2.15. Any value greater than that indicates that the hypothesis of a straight-line model for this data should be rejected.