1.4.2.5.4. Validate New Model

1. Exploratory Data Analysis
1.4. EDA Case Studies
1.4.2. Case Studies
1.4.2.5. Beam Deflections

1.4.2.5.4. Validate New Model

The first step in evaluating the fit is to generate a 4-plot of the residuals.

Interpretation

The assumptions are addressed by the graphics shown above:

The run sequence plot (upper left) indicates that the data do not have any significant shifts in location. There does seem to be some shifts in scale. A start-up effect was detected previously by the complex demodulation amplitude plot. There does appear to be a few outliers.
The lag plot (upper right) shows that the data are random. The outliers also appear in the lag plot.
The histogram (lower left) and the normal probability plot (lower right) do not show any serious non-normality in the residuals. However, the bend in the left portion of the normal probability plot shows some cause for concern.

The 4-plot indicates that this fit is reasonably good. However, we will attempt to improve the fit by removing the outliers.

Fit Output with Outliers Removed

Dataplot generated the following fit output after removing 3 outliers.

 LEAST SQUARES NON-LINEAR FIT
       SAMPLE SIZE N =      197
       MODEL--Y =C + AMP*SIN(2*3.14159*FREQ*T + PHASE)
       NO REPLICATION CASE
  
 ITERATION  CONVERGENCE  RESIDUAL  *  PARAMETER
  NUMBER      MEASURE    STANDARD  *  ESTIMATES
                         DEVIATION *
 ----------------------------------*-----------
     1--  0.10000E-01  0.14834E+03 *-0.17879E+03-0.36177E+03 0.30260E+00 0.14654E+01
  
     2--  0.37409E+02  0.14834E+03 *-0.17879E+03-0.36176E+03 0.30260E+00 0.14653E+01
  
         FINAL PARAMETER ESTIMATES           (APPROX. ST. DEV.)    T VALUE
        1  C                   -178.788       ( 10.57    )       -16.91
        2  AMP                 -361.759       ( 25.45    )       -14.22
        3  FREQ                0.302597       (0.1457E-03)        2077.
        4  PHASE                1.46533       (0.4715E-01)        31.08
  
       RESIDUAL    STANDARD DEVIATION =         148.3398
       RESIDUAL    DEGREES OF FREEDOM =         193

New Fit to Edited Data

The original fit, with a residual standard deviation of 155.84, was:

The new fit, with a residual standard deviation of 148.34, is:

There is minimal change in the parameter estimates and about a 5% reduction in the residual standard deviation. In this case, removing the residuals has a modest benefit in terms of reducing the variability of the model.

4-Plot for New Fit

This plot shows that the underlying assumptions are satisfied and therefore the new fit is a good descriptor of the data.

In this case, it is a judgment call whether to use the fit with or without the outliers removed.