Reason for Using RMSE Instead of MSE in Linear Regression

Answer: RMSE is preferred over MSE in linear regression because it is in the same units as the response variable, making interpretation easier.

In linear regression analysis, both the Mean Squared Error (MSE) and the Root Mean Squared Error (RMSE) serve as measures to evaluate model performance, specifically regarding how well the model predicts the dependent variable. However, RMSE is often preferred over MSE for several reasons, primarily due to its interpretability.

Comparison Between MSE and RMSE:

Metric	Description	Advantages
MSE	The average of the squares of the errors between the predicted and actual values.	Directly related to the model fit, easy to compute, differentiable (useful for optimization).
RMSE	The square root of MSE.	In the same units as the response variable, making it easier to interpret and relate to the problem.

Key Reasons for Preferring RMSE:

• Interpretability: RMSE is expressed in the same units as the target variable, simplifying the interpretation of the model’s prediction accuracy.
• Sensitivity to Large Errors: RMSE increases more with larger errors due to the squaring before the root, emphasizing significant discrepancies between predicted and actual values.

Conclusion:

While both MSE and RMSE are valuable metrics for assessing the performance of linear regression models, RMSE is often preferred due to its interpretability in the same units as the dependent variable. This characteristic makes it easier for stakeholders to understand the magnitude of prediction errors, facilitating more informed decisions based on the model’s outputs.