Which selection method would most likely terminate when no significant improvement can be made?

The answer identifies all three methods—forward selection, backward selection, and stepwise selection—as terminating when no significant improvement can be made.

Forward selection builds a model by adding predictors one at a time, where each predictor is chosen based on its statistical significance in improving the model’s fit. The process continues until no additional predictor can significantly enhance the model.

Backward selection, on the other hand, starts with all available predictors and removes them one at a time. Similar to forward selection, it evaluates whether removing a predictor significantly degrades the model. The process halts when removing any further predictors does not lead to a significant loss of model performance.

Stepwise selection incorporates elements of both forward and backward selection. It begins by adding or removing predictors based on their significance, allowing for both the inclusion and exclusion of variables to optimize the model.

All three methods are designed to identify the most important predictors and optimize model performance, ceasing their operations when any potential additions or removals do not result in significant enhancement of the model. This characteristic makes the answer comprehensive, as it reflects the termination condition common to all three methods.