The correct answer is: C. both
Stepwise forward selection and stepwise backward elimination are both possible methods to select the best $x$ models for an ensemble. Stepwise forward selection starts with an empty model and adds variables one at a time until the model stops improving. Stepwise backward elimination starts with a full model and removes variables one at a time until the model stops getting worse.
Both methods can be used to select the best $x$ models for an ensemble, but they have different advantages and disadvantages. Stepwise forward selection is more likely to select the best models, but it is also more likely to overfit the data. Stepwise backward elimination is less likely to overfit the data, but it is also more likely to select suboptimal models.
In general, it is best to use a combination of both methods to select the best $x$ models for an ensemble. This can be done by starting with a full model and then using stepwise backward elimination to remove any variables that are not significantly contributing to the model. The remaining variables can then be used as the basis for a stepwise forward selection procedure. This approach will help to ensure that the selected models are both accurate and robust.
Here is a more detailed explanation of each option:
- A. Stepwise forward selection
Stepwise forward selection is a statistical method for selecting the best subset of variables from a set of candidate variables. The method starts with an empty model and adds variables one at a time until the model stops improving. The improvement is measured by a statistical test, such as the F-test or the t-test.
Stepwise forward selection is a powerful method for selecting the best subset of variables, but it can be prone to overfitting the data. Overfitting occurs when the model fits the training data too well and does not generalize well to new data. To avoid overfitting, it is important to use a cross-validation procedure to evaluate the model.
- B. Stepwise backward elimination
Stepwise backward elimination is a statistical method for selecting the best subset of variables from a set of candidate variables. The method starts with a full model and removes variables one at a time until the model stops getting worse. The improvement is measured by a statistical test, such as the F-test or the t-test.
Stepwise backward elimination is a powerful method for selecting the best subset of variables, but it can be prone to underfitting the data. Underfitting occurs when the model does not fit the training data well enough. To avoid underfitting, it is important to use a cross-validation procedure to evaluate the model.
- C. Both
Both stepwise forward selection and stepwise backward elimination can be used to select the best $x$ models for an ensemble. However, they have different advantages and disadvantages. Stepwise forward selection is more likely to select the best models, but it is also more likely to overfit the data. Stepwise backward elimination is less likely to overfit the data, but it is also more likely to select suboptimal models.
In general, it is best to use a combination of both methods to select the best $x$ models for an ensemble. This can be done by starting with a full model and then using stepwise backward elimination to remove any variables that are not significantly contributing to the model. The remaining variables can then be used as the basis for a stepwise forward selection procedure. This approach will help to ensure that the selected models are both accurate and robust.