Which modeling technique guarantees the identification of the best model for a specific number of variables?

Best-subsets regression is a modeling technique that systematically evaluates all possible combinations of predictor variables to identify the model that provides the best fit for the data based on a specific criterion, such as the lowest Akaike Information Criterion (AIC) or the highest adjusted R-squared value. This comprehensive approach ensures that for a given number of variables, the model selected is optimal in terms of balancing model complexity and goodness of fit.

In contrast, the other techniques mentioned—stepwise regression, forward selection, and least squares regression—do not guarantee finding the best model for a specific number of variables. Stepwise and forward selection methods involve adding or removing variables based on certain criteria but may not assess all combinations, potentially missing the optimal model. Least squares regression by itself pertains to the method used for estimating the parameters of the model and does not address model selection directly. Thus, best-subsets regression stands out as the technique that thoroughly explores the possibility space to ensure the best model is identified for a defined set of variables.