 4. Process Modeling
4.6. Case Studies in Process Modeling
4.6.4. Thermal Expansion of Copper Case Study

## 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.
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```   1. Read in the data.

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``` 1. You have read 2 columns of numbers
into Dataplot, variables thermexp
and temp.
```
```2. Plot the data.
```
```   1. Plot thermexp versus temp.

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```
```
``` 1. Initial plot indicates that a
nonlinear model is required.

```
```4. Fit a Q/Q rational function model.
```
```   1. Perform the Q/Q fit and plot the
predicted values with the raw data.

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```   2. Perform model validation by
generating a 6-plot.

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```   3. Generate a full-sized plot of the
residuals to show greater detail.

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``` 1. The model parameters are estimated.
The plot of the predicted values with
the raw data seems to indicate a
reasonable fit.
```
``` 2. The 6-plot shows that the
pattern and suggests that the
randomness assumption for the
errors is violated.
```
``` 3. The full-sized residual plot shows
the non-random pattern more
clearly.

```
```3. Fit a C/C rational function model.
```
```   1. Perform the C/C fit and plot the
predicted values with the raw data.

```
```   2. Perform model validation by
generating a 6-plot.

```
```   3. Generate a full-sized plot of the
residuals to show greater detail.

```
```
```
``` 1. The model parameters are estimated.
The plot of the predicted values with
the raw data seems to indicate a
reasonable fit.
```
``` 2. The 6-plot does not indicate any
notable violations of the
assumptions.

```
``` 3. The full-sized residual plot shows
no notable assumption violations.

``` 