In predicting multiple variables, what method explains variance starting with the best predictor and exhausts its power before moving to the next?

The method that explains variance by starting with the best predictor and then exhausts its power before moving to the next is known as Stepwise Multiple Regression. This technique systematically adds or removes variables based on statistical criteria, effectively optimizing the model to predict the outcome variable.

In Stepwise Multiple Regression, the procedure begins with no predictors and assesses the variables to identify which one has the strongest correlation with the dependent variable. Once the first predictor is included, the model tests the remaining variables to determine if adding them will significantly improve the model's predictive power. If the addition does not meet the specified criteria, it remains excluded. This method ensures that only the most relevant variables are utilized in creating a robust predictive model.

The other methods mentioned do have their own unique processes and applications, but they do not operate in the same manner as Stepwise Multiple Regression. Hierarchical Regression is used to assess the impact of variables in a predetermined order, but it does not necessarily focus on exhaustively determining the best predictor's power first. Backward Regression starts with all potential predictors and removes them iteratively, while Forward Regression adds them one at a time, neither of which prioritize the power of the best predictor in the same systematic way.