The final answer is: There is no one-size-fits-all solution. However, here are some general guidelines for model selection and interpretation of the results:

1. When leaps returns only poly(X, 2)1, you can safely drop higher-order terms: This means that you can fit a linear model without any polynomial terms.

2. Retain poly(X, 2)1 in your model whenever possible: This term represents the first order interaction between X and its square. Including this term ensures that you are not losing any important information about non-linear relationships between X and the response variable.

3. If a higher-order term is dropped by leaps, but the lower-order term associated with it is retained, consider keeping both terms in your model: This ensures that you are not losing any important information about non-linear relationships between X and the response variable.

4. Consider fitting a higher-order polynomial if only the first order interaction is retained by leaps: In this case, you might be able to uncover more complex patterns in the data with a model that includes higher-order interactions.

5. Use your best judgment when interpreting the results: Consider the context of the problem and the characteristics of the data. Make sure to include terms that are statistically significant and that make interpretative sense.

In summary, while there is no one-size-fits-all solution, these guidelines can help you navigate the process of selecting a model from leaps. Ultimately, it’s essential to use your knowledge of statistics and machine learning concepts, as well as domain-specific expertise, to guide your decision-making.

Last modified on 2023-11-08