4.6.3.6. Work This Example Yourself

4. Process Modeling
4.6. Case Studies in Process Modeling
4.6.3. Ultrasonic Reference Block Study

4.6.3.6. 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 ultrason and metal.
2. Plot data, pre-fit for starting values, and fit nonlinear model. 1. Plot ultrason versus metal. 2. Run PREFIT to generate good starting values. 3. Nonlinear fit of ultrason versus metal. Plot predicted values with the data. 4. Generate a 6-plot for model validation. 5. Plot the residuals against the predictor variable.	1. Initial plot indicates that a nonlinear model is required. Theory dictates an exponential over linear for the inital model. 2. Pre-fit indicated starting values of 0.1 for all 3 parameters. 3. The nonlinear fit was carried out. Inital fit looks pretty good. 4. The 6-plot shows that the model assumptions are satisfied except for the non-homogeneous variances for the residuals. 5. The detailed residual plot shows the non-homogeneous variances more clearly.
3. Improve the fit with transformations. 1. Plot several common transformations of the dependent variable (ultrasonic response) data. 2. Plot several common transformations of the predictor variable (metal). 3. Nonlinear fit of transformed data. Plot predicted values with the data. 4. Generate a 6-plot for model validation. 5. Plot the residuals against the predictor variable.	1. The plots indicate that a square root transformation on the dependent variable (ultrasonic response) is a good candidate model. 2. The plots indicate that no transformation on the predictor variable (ultrasonic response) is a good candidate model. 3. Carry out the fit on the transformed data. The plot of the predicted values with the data indicate a good fit. 4. The 6-plot shows that the model assumptions, specifically homogeneous variances for the residuals, are satisfied. 5. The detailed residual plot shows more clearly that the homogeneous variances assumption is now satisfied.
4. Improve the fit using weighting. 1. Fit function to determine appropriate weight function. Determine value for c in the power model. 2. Residuals from fit to determine appropriate weight function. 3. Weighted linear fit of field versus lab. Plot predicted values with the data. 4. Generate a 6-plot for model validation. 5. Plot the residuals against the predictor variable.	1. The fit to determine an appropriate weight function indicates that a value of c in the range -1.0 to -1.1 should be reasonable. 2. The residuals from this fit indicate no major problems. 3. The weighted fit was carried out. The plot of the predicted values with the data indicates that we now have homogeneous variances. 4. The 6-plot shows that the model assumptions are satisfied. 5. The detailed residual plot shows the homogeneous variances for the residuals more clearly.
5. Compare the fits. 1. Plot predicted values from each of the three models with the data.	1. The transformed and weighted fits generate only slightly different predicted values, but the model assumptions are not violated.