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


4Plot of Residuals

The first step in
evaluating the fit
is to generate a 4plot
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 startup 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 nonnormality in
the residuals. However, the bend in the left portion of the
normal probability plot shows some cause for concern.
The 4plot indicates that this fit is reasonably good. However,
we will attempt to improve the fit by removing the outliers.

Fit Results with Outliers Removed

The following parameter estimates were obtained after removing three
outliers.
Coefficient Estimate Stan. Error tValue
C 178.788 10.57 16.91
AMP 361.759 25.45 14.22
FREQ 0.302597 0.1457E03 2077.00
PHASE 1.46533 0.4715E01 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:
\( \hat{Y}_i = 178.786  361.766[2\pi(0.302596)T_i + 1.46536] \)
The new fit, with a residual standard deviation of 148.34, is:
\( \hat{Y}_i = 178.788  361.759[2\pi(0.302597)T_i + 1.46533] \)
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.

4Plot 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.
