XLSTAT: RIDGE regression

 

Dataset for Example

The original data are from Osborne and al. (1984). The dataset contains, for 30 cookies, the discretizations of near-infrared spectra. Each spectrum is observed at wavelengths ranging from 1100 to 2460 nanometers and spaced by 40 nanometers, which leads to 35 explanatory variables in the dataset. The data table also contains the water composition of each cookie.

The goal of this tutorial is to set up and interpret a Ridge regression in order to predict the water composition of the different cookies.

 

Setting Up 

• Open XLSTAT.

• Click on the Modeling data menu and select the Ridge regression feature.

In the General tab:

• Select the water composition of the cookies as the Dependent variable  (or variable to model).

• Select all columns numbered L1 to L35 as the Quantitative explanatory variables. Here we want to explain the variability of the water content in the cookies as a function of the spectrum.

• Select the first 20 cookies from the dataset to be included in the modeling, the others will be used for prediction.

• Check the Variable labels checkbox to display the name of each variable at the top of the table.

• Check the Observation labels box and select the name of the different cookies.

In the Options tab:

• Use Cross-validation to find the optimal lambda regularization parameter.

• Choose to form 5 folds for the cross-validation and to test 100 lambda values.

• In the Prediction tab, select the data on which you want to get a prediction. Here we select the last 10 cookies in the dataset.

• In the Charts tab, activate the option Evolution of the MSE (Cross-validation) to visualize the evolution of the MSE (Mean Squared Error) depending on the regularization parameter.

• Click on the OK button to launch the computations.

• The results are displayed on a new Excel sheet.

 

Interpreting the Results

The table “Model parameters” gives details on the model. This table is helpful when predictions are needed or to analyze the importance of variables in the model. We see that all 35 variables were kept in the modeling with low-value and relatively homogeneous coefficients.

 

The following chart shows the evolution of the MSE depending on the Lambda regularization parameter. The Lambda value selected by XLSTAT is the one that minimizes the MSE, that is to say, here approximately 0.133.

 

The last table gives, following the estimation of the model, the predictions of the water composition of the 10 cookies used in the prediction dataset.

 

 

 Conclusion

Finally, distinct from LASSO regression, Ridge regression has modeled the water composition of the different cookies with all 35 variables available. At the same time, unlike the LASSO regression, no variable really stands out with a large coefficient in the modeling constructed by the Ridge regression.