4.6.1.9. Interpretation of Numerical Output

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

4.6.1.9. Interpretation of Numerical Output - Model #2

Quadratic Confirmed

The numeric results from the fit are shown below. For the quadratic model, the lack-of-fit test statistic is 0.8107. The fact that the test statistic is approximately one indicates there is no evidence to support a claim that the functional part of the model does not fit the data. The test statistic would have had to have been to greater than 2.17 to reject the hypothesis that the quadratic model is correct.

Dataplot Output

 
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

Regression Function

From the numeric output, we can also find the regression function which will be used for the calibration. The function, with its estimated parameters, is

All of the parameters are significantly different from zero, as indicated by the associated t statistics. The 97.5% cut-off for the t distribution with 37 degrees of freedom is 2.026. Since all of the t values are well above this cut-off, we can safely conclude that none of the estimated parameters is equal to zero.