XLSTAT: Training a support vector machine for regression (SVR)

 

Dataset for Example

The attached abalone dataset includes characteristics of abalones. Since counting rings to determine age is time-consuming, the goal is to predict age using easier-to-measure features.

 

Setting Up

• Open XLSTAT.

• Click on the Machine Learning menu and select the Support Vector Machine feature.

 

After clicking the button, the SVM dialog box opens.

In the General tab:

• • Select the quantitative Response Variable (number of rings).

  • Choose Quantitative as the response type for regression.

  • Check both quantitative and qualitative explanatory variables.

  • In Quantitative, select Length, Diameter, and Height.

  • In Qualitative, select Sex.

  • Check Variable labels since variable names are in the table header.

In the Options tab:

• Keep default SMO settings.

• Set C (regularization) to 1 (must be positive).

• Leave Tolerance at default (higher values speed up computation).

• Leave Epsilon at default (must be positive).

• Choose Standardisation for preprocessing.

• Use linear kernels.

In the Validation tab:

Check Validation and select 10 random observations from the training sample to evaluate the regression model’s performance.

In the Outputs tab:

• Select the outputs we want to obtain as shown below:

• Click on the OK button to launch the computations.

• The results are displayed on a new Excel sheet.

 

Interpreting the Results

The first table shows regression performance metrics: mean squared error, mean absolute error, and coefficient of determination.

A low error and an R² close to 1 indicate good fit. The validation set’s R² is 71%.

The second table summarizes the optimized SVR: 70 observations trained, 59 support vectors identified, and the bias (hyperplane origin) used for predicting the validation sample.

The next table shown below gives the complete list of the 59 supports vectors with the associated alpha-alpha* coefficient values , values of the response variable, scaled explanatory variables and the disjunctive matrix of qualitative variables.

Finally, you can see predicted values obtained by the regression for each observation on the figure below: