4. Process Modeling
4.6. Case Studies in Process Modeling

Work This Example Yourself

View Dataplot Macro for this Case Study This page allows you to repeat the analysis outlined in the case study description on the previous page using Dataplot, if you have downloaded and installed it. Output from each analysis step below will be displayed in one or more of the Dataplot windows. The four main windows are the Output window, the Graphics window, the Command History window and the Data Sheet window. Across the top of the main windows there are menus for executing Dataplot commands. Across the bottom is a command entry window where commands can be typed in.
Data Analysis Steps Results and Conclusions

Click on the links below to start Dataplot and run this case study yourself. Each step may use results from previous steps, so please be patient. Wait until the software verifies that the current step is complete before clicking on the next step.

The links in this column will connect you with more detailed information about each analysis step from the case study description.

```1. Get set up and started.
```
```   1. Read in the data.

```
```
```
``` 1. You have read 2 columns of numbers
into Dataplot, variables Deflection
```
```2. Fit and validate initial model.
```
```   1. Plot deflection vs. load.

```
```   2. Fit a straight-line model
to the data.

```
```   3. Plot the predicted values
from the model and the
data on the same plot.
```
```   4. Plot the residuals vs.

```
```   5. Plot the residuals vs. the
predicted values.
```
```   6. Make a 4-plot of the
residuals.
```
```   7. Refer to the numerical output
from the fit.

```
```
```
``` 1. Based on the plot, a straight-line
model should describe the data well.
```
``` 2. The straight-line fit was carried
out.  Before trying to interpret the
numerical output, do a graphical
residual analysis.
```
``` 3. The superposition of the predicted
and observed values suggests the
model is ok.
```
``` 4. The residuals are not random,
indicating that a straight line
```
``` 5. This plot echos the information in
the previous plot.
```
``` 6. All four plots indicate problems
with the model.
```
``` 7. The large lack-of-fit F statistic
(>214) confirms that the straight-
```
```3. Fit and validate refined model.
```
```   1. Refer to the plot of the

```
```   2. Fit a quadratic model to
the data.

```
```   3. Plot the predicted values
from the model and the
data on the same plot.
```
```   4. Plot the residuals vs. load.

```
```   5. Plot the residuals vs. the
predicted values.

```
```   6. Do a 4-plot of the
residuals.
```
```   7. Refer to the numerical
output from the fit.

```
```
```
``` 1. The structure in the plot indicates
describe the data.
```
``` 2. The quadratic fit was carried out.
Remember to do the graphical
residual analysis before trying to
interpret the numerical output.
```
``` 3. The superposition of the predicted
and observed values again suggests
the model is ok.
```
``` 4. The residuals appear random,
suggesting the quadratic model is ok.
```
``` 5. The plot of the residuals vs. the
predicted values also suggests the
```
``` 6. None of these plots indicates a
problem with the model.
```
``` 7. The small lack-of-fit F statistic
model fits the data.
```
```4. Use the model to make a calibrated
measurement.
```
```   1. Observe a new deflection
value.
```
```   2. Determine the associated

```
```   3. Compute the uncertainty of

```
```

```
``` 1. The new deflection is associated with
``` 2. Solving the calibration equation
``` 3. Computing a confidence interval for