Fitting Linear Models • Standard Least Squares Report and Options • Fit Least Squares Report
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Fit Least Squares Report
When you fit a model using the Standard Least Squares personality, you obtain a Fit Least Squares report. The content of the report is driven by the nature of the data and your selections in the Fit Model launch window.
Tip: To always see reports that do not appear by default, select them using File > Preferences > Platforms > Fit Least Squares.
Single versus Multiple Responses
When you fit a single response variable Y, the Fit Least Squares window organizes detailed reports in a report entitled “Response Y”. When you fit several responses, reports for individual responses are usually organized in a report entitled “Least Squares Fit”. However, if there is missing response data, and you select the option to Fit Separately, reports for individual responses are organized in a report titled “Fit Group”.
Report Structure Related to Emphasis
When you select the Effect Leverage Emphasis in the Fit Model launch window, the report for a given response is arranged in columns. The left column consists of the Whole Model report, which contains additional reports that pertain to the model. Reports for each effect in the model are shown in the columns to the right of the Whole Model report.
When you select either the Effect Screening or Minimal Report Emphasis in the Fit Model launch window, all reports for each response are arranged in the left column.
Special Reports
This section describes the reports that are available based on the data structure or choices that you made regarding effect attributes.
Singularity Details
When there are linear dependencies among model effects, the Singularity Details report appears as the first report under the Response report title. It displays the linear functions that the model terms satisfy. These functions define the aliasing relationships among model terms. Singularity Details Report shows an example for the Singularity.jmp sample data table.
Singularity Details Report
When there are linear dependencies among effects, estimates of some model terms are not unique. See Models with Linear Dependencies among Model Terms.
Response Surface Report
When an effect in a model has the response surface (&RS) or mixture response surface (&RS&Mixture) attribute, a Response Surface report is provided. See Response Surface Report for an example of a Response Surface report for the Tiretread.jmp sample data table.
Response Surface Report
Matrix of Second-Order Terms
The Coef table shows parameter estimates for the second-order model terms. The table provides you with a concise summary of the estimated model parameters.
Solution Report
The Solution report gives a critical value (maximum, minimum, or saddle point), if one exists, along with the predicted value at that point. It also alerts you if the solution falls outside the range of the data.
Canonical Curvature Report
The eigenvalues and eigenvectors of the matrix of second-order parameter estimates determine the type of curvature. The eigenvectors show the principal directions of the surface, including the directions of greatest and smallest curvature.
The eigenvalues are provided in the first row of the Canonical Curvature table.
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If the eigenvalues are negative, the response surface curves downward from a maximum.
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If the eigenvalues are positive, the surface shape curves upward from a minimum.
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If there are both positive and negative eigenvalues, the surface is saddle shaped, curving up in one direction and down in another direction. See Surface Profiler Plot with Saddle-Shaped Surface for an example using the Tiretread.jmp sample data table.
Surface Profiler Plot with Saddle-Shaped Surface
The eigenvectors listed below the eigenvalues show the orientation of the principal axes. The larger the absolute value of an eigenvalue, the greater the curvature of the response surface in its associated direction. Sometimes a zero eigenvalue occurs. This eigenvalue means that, along the direction described by the corresponding eigenvector, the fitted surface is flat.
Note: The response surface report is not shown for response surface models consisting of more than 20 factors. No error message or alert is given. For more information about response surface designs, see the Design of Experiments Guide book.
Mixed and Random Effect Model Reports
When you specify a random effect in the Fit Model launch window, the Method list appears. This list provides two fitting methods: REML (Recommended) and EMS (Traditional). Additional reports as well as Save Columns and Profiler options are shown, based on the model and the method that you select.
For details about the REML method reports, see Restricted Maximum Likelihood (REML) Method. For details about the EMS method reports, see EMS (Traditional) Model Fit Reports.
Least Squares Fit Options
You might have more than one Y and no missing response values, or more than one Y with missing values. When you select Fit Together, the responses are grouped in a report called Least Squares Fit. The red triangle menu includes the following options:
Profilers
Shows all responses in a single profiler. You can view the effects of model terms on all responses simultaneously and perform multiple optimization. See Factor Profiling.
Model Dialog
Shows the completed launch window for the current analysis.
Effect Summary
Shows the interactive Effect Summary report that enables you to add or remove effects from the model. See Examples of Model Specifications and Their Model Fits.
Script
Contains options that are available to all platforms. See the Using JMP book.
Fit Group Options
When you have more than one Y and you select Fit Separately, the responses are grouped in a report called Fit Group. The red triangle menu includes the following options:
Profiler
Shows all responses in a single profiler. You can view the effects of model terms on all responses simultaneously and perform multiple optimization. See Profiler.
Contour Profiler
Shows all responses in a single contour profiler. You can explore the effects of model terms on all responses simultaneously.
Surface Profiler
Shows separate surface profiler reports for each response.
Arrange in Rows
Rearranges the reports for the platform analyses in a specified number of rows. This would be used mostly to arrange reports so that more reports fit in a window or on the page of output.
Order by Goodness of Fit
Sorts the reports by significance of fit (RSquare). This option is only available for platforms that surface the RSquare to the platform level. For example, if you have hundreds of Oneway analyses generated from one launch window, they will appear in a FitGroup and you can sort them so that the strongest relationships appear first.
Script
Contains options that are available to all platforms. See the Using JMP book.
For details about the JMP profilers, see Profilers.