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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 model is a good 
    initial 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 initial fit looks good,
    the plot indicates that the residuals
    do not have homogeneous variances.
 2. The 6-plot does not indicate any 
    other problems with the model,
    beyond the evidence of 
    non-constant error variance.
 3. The detailed residual plot shows
    the inhomogeneity of the error
    variation more clearly.
4. Improve the fit with transformations.
   1. Plot several common transformations
      of the response variable (field)
      versus the predictor variable (lab).

   2. Plot ln(field) versus several 
      common transformations of the 
      predictor variable (lab).
     
   3. Box-Cox linearity plot.



   4. Linear fit of ln(field) versus 
      ln(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 ln
    transformation of the dependent
    variable (field) stabilizes
    the variation.
 2. The plots indicate that a ln
    transformation of the predictor
    variable (lab) linearizes the 
    model.
 3. The Box-Cox linearity plot
    indicates an optimum transform
    value of -0.1, although a ln
    transformation should work well.
 4. The plot of the predicted values
    with the data indicates that
    the errors should now have
    homogeneous variances.

 5. The 6-plot shows that the model
    assumptions are satisfied.

 6. The detailed residual plot shows
    more clearly that the assumption
    of homogeneous variances is now 
    satisfied.
5. Improve the fit using weighting.
   1. Fit function to determine appropriate
      weight function.  Determine value for
      the exponent in the power model.

   2. Examine residuals from weight fit 
      to check adequacy of weight function.
   3. Weighted linear fit of field versus
      lab.  Plot predicted values with
      the data.

   4. Generate a 6-plot after weighting
      the residuals for model validation.
   5. Plot the weighted residuals 
      against the predictor variable.


 1. The fit to determine an appropriate
    weight function indicates that a
    an exponent between 1.5 and 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 the
    fit of the model is improved.
 4. The 6-plot shows that the model
    assumptions are satisfied.
 5. The detailed residual plot shows
    the constant variability of the
    weighted residuals.
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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