When comparing regression models, which factor might lead you to select Model Y despite having a higher Mean Squared Error than Model X?

Selecting Model Y, despite its higher Mean Squared Error (MSE) compared to Model X, can be justified if Model Y has a higher R² value. R² (coefficient of determination) is a statistical measure that indicates how well the independent variables explain the variability of the dependent variable. A higher R² means that a greater proportion of the variability in the outcome can be explained by the model, which is often an indicator of the model's relevance and effectiveness in representing the underlying relationships in the data.

In the context of model selection, it's important to evaluate both prediction accuracy (which MSE reflects) and how well the model captures the patterns within the data. While a lower MSE indicates fewer prediction errors on average, it does not fully reflect the model's ability to explain variance. Therefore, if Model Y offers a more comprehensive understanding of the data's structure or more relevant insights due to a higher R², it could be preferred over Model X, even if it has a higher MSE. This situation often arises in cases where a model's complexity allows for nuanced relationships in the data that are otherwise missed, underscoring the importance of considering both predictive performance and explanatory power when comparing regression models.