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4. Process Modeling
4.6. Case Studies in Process Modeling
4.6.2. Alaska Pipeline

4.6.2.7.

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 3 columns of numbers 
    into Dataplot, variables Field,
    Lab, and Batch.
2. Plot data and check for batch effect.
   1. Plot field versus lab.


   2. Condition plot on batch.


   3. Check batch effect with.
      linear fit plots by batch.

                              
 1. Initial plot indicates that a
    simple linear fit is a good 
    inital model.
 2. Condition plot on batch indicates
    no significant batch effect.

 3. Plots of fit by batch indicate no
    significant batch effect.

3. Fit and validate initial model.
   1. Linear fit of field versus lab.
      Plot predicted values with the
      data.

   2. Generate a 6-plot for model
      validation.


   3. Plot the residuals against
      the predictor variable.


 1. The linear fit was carried out.
    Although the inital fit looks good,
    the plot indicates that the residuals
    do not have homogeneous variances.
 2. The 6-plot shows that the model
    assumptions are satisfied except for
    the non-homogeneous variances for
    the residuals.
 3. The detailed residual plot shows
    the non-homogeneous variances
    more clearly.
4. Improve the fit with transformations.
   1. Plot several common transformations
      of the dependent variable (field).
      data.

   2. Plot several common transformations
      of the predictor variable (lab).


   3. Box-Cox linearity plot.



   4. Linear fit of field versus lab.
      Plot predicted values with the
      data.


   5. Generate a 6-plot for model
      validation.


   6. Plot the residuals against
      the predictor variable.


 1. The plots indicate that a log
    transformation on the dependent
    variable (field)is a good candidate
    model.
 2. The plots indicate that a log
    transformation on the predictor
    variable (lab)is a good candidate
    model.
 3. The Box-Cox linearity plot
    indicates an optimum transform
    value of 0.6, although a log
    transformation should work well.
 4. Carry out the log-log fit.
    The plot of the predicted values
    with the data indicate that
    the residuals should have
    homogeneous variances.
 5. The 6-plot shows that the model
    assumptions are satisfied.


 6. The detailed residual plot shows
    more clearly that the homogeneous
    variances assumption is now
    satisfied.
5. 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 1.5 to 2.0
    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.
6. Compare the fits.
   1. Plot predicted values from each
      of the three models with the 
      data.



 1. The transformed and weighted fits
    generate lower predicted values for
    low values of defect size and larger
    predicted values for high values of
    defect size.
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