HS-1705: Simple Fit Study

Learn how to set up a space filling DOE study, and then set up a Fit.

Before you begin, complete HS-1700: Simple DOE Study or import the HS-1700.hstx archive file, available in <hst.zip>/HS-1705/.
The base input template defines two input variables; DV1 and DV2, labeled X and Y, respectively. The objective of the study is to investigate the two input variables X, Y forming the two functions: X+Y and 1/X + 1/Y – 2.

Run Doe

  1. Add a DOE.
    1. In the Explorer, right-click and select Add from the context menu.
    2. In the Add dialog, select DOE and click OK.
  2. Define specifications.
    1. Go to the DOE 2 > Specifications step.
    2. In the work area, set the Mode to Hammersley.
    3. Click Apply.
  3. Evaluate tasks.
    1. Go to the DOE 2 > Evaluate step.
    2. Click Evaluate Tasks.
      The results of the evaluation display in the work area.
  4. Go to the DOE 2 > Post-Processing step.
  5. View a plot which illustrates the dependency between Area 2 and Response 1 and Response 2.
    1. Click the Scatter tab.
    2. Using the Channel selector, set the X Axis to Area 2 and the Y Axis to both Response 1 and Response 2.
    3. Compare the scatter plots to determine if the runs are distributed homogeneously throughout the design space.


      Figure 1.

Run Fit

  1. Add a Fit.
    1. In the Explorer, right-click and select Add from the context menu.
    2. In the Add dialog, select Fit and click OK.
  2. Import matrix.
    1. Go to the Fit 1 > Specifications step.
    2. Click Add Matrix.
    3. In the work area, set Matrix Source to Doe 2 (doe_2).
    4. Click Apply.


    Figure 2.
  3. Define specifications.
    1. In the work area, Fit Type column, select Least Squares Regression (LSR) for both output responses.
    2. Click Apply.


    Figure 3.
  4. Evaluate tasks.
    1. Go to the Fit 1 > Evaluate step.
    2. Click Evaluate Tasks.
  5. Post process results.
    1. Go to the Fit 1 > Post-Processing step.
    2. Click the Residuals tab and review the residuals of both output responses.

      The data in the table shows the differences in the actual values and the predictions from the constructed Fit. The Percent Error column of Response_1 is numerically zero for all six runs; whereas the Percent Error column of Response_2 is up to 35%. The LSR fitting for Response_1 is acceptable, but the LSR fitting for Response_2 is rather large.

    3. Click the Diagnostics tab and review the overall Fit quality.

      Several measures are shown to indicate the relative quality of the Fit. The R-Square value can be interpreted as the percentage of variance in the data that can be explained by the Fit.

      For Response_1, the Fit captures 100% of the data variance; this makes sense as Response_1 is actually a linear function so the first order regression matches the actual data with no error. For Response_2, it is shown below that the Fit explains about 90% of the variance.


      Figure 4.
  6. Go back to the Specifications step and try different methods until you find an acceptable fitting for both output responses.
    With first order least squares, you have a Fit which explains most of the data’s variance, but it still has a relatively high prediction error.