Which of the following possible explanations for this difference is invalid?

A data scientist has created two linear regression models. The first model uses price as a label variable and the second model uses log(price) as a label variable. When evaluating the RMSE of each model by comparing the label predictions to the actual price values, the data scientist notices that the RMSE for the second model is much larger than the RMSE of the first model.

Which of the following possible explanations for this difference is invalid?
A . The second model is much more accurate than the first model
B . The data scientist failed to exponentiate the predictions in the second model prior to computing the RMSE
C . The data scientist failed to take the log of the predictions in the first model prior to computing the RMSE
D . The first model is much more accurate than the second model
E . The RMSE is an invalid evaluation metric for regression problems

Answer: E

Explanation:

The Root Mean Squared Error (RMSE) is a standard and widely used metric for evaluating the accuracy of regression models. The statement that it is invalid is incorrect. Here’s a breakdown of why the other statements are or are not valid:

Transformations and RMSE Calculation: If the model predictions were transformed (e.g., using log), they should be converted back to their original scale before calculating RMSE to ensure accuracy in the evaluation. Missteps in this conversion process can lead to misleading RMSE values.

Accuracy of Models: Without additional information, we can’t definitively say which model is more accurate without considering their RMSE values properly scaled back to the original price scale.

Appropriateness of RMSE: RMSE is entirely valid for regression problems as it provides a measure of how accurately a model predicts the outcome, expressed in the same units as the dependent variable.

Reference

"Applied Predictive Modeling" by Max Kuhn and Kjell Johnson (Springer, 2013), particularly the chapters discussing model evaluation metrics.