For a dataset with equal predictors and observations, which statement is true?

In the context of model selection using stepwise regression techniques, it is important to understand how the number of predictors relates to the number of observations in a dataset. When the number of predictors equals the number of observations, the ability to conduct model selection through backward stepwise selection becomes constrained.

Backward stepwise selection starts with a full model that includes all predictors and iteratively removes the least significant predictors to arrive at a more parsimonious model. However, in a situation where the number of predictors equals the number of observations, removing even one predictor can lead to an underfitting problem since you would ultimately end up with a model that is too simple to accurately capture the variance in the data. This is particularly relevant when trying to estimate the coefficients of a model, as each predictor requires enough observations to provide a reliable estimate.

Therefore, the assertion that backward stepwise selection cannot be used in a dataset where the number of predictors equals the number of observations is accurate because it would not have enough degrees of freedom to effectively evaluate the necessity of predictor variables without risking a poorly fitted model.

On the other hand, forward stepwise selection begins with no predictors and adds them based on their significance, making it more adaptable to scenarios where the predictors might equal the observations