Regression Rivalry: MSE vs. MAE vs. RMSE — Which is the Best Metric?

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Delve into the world of regression error metrics, comparing Mean Squared Error (MSE), Mean Absolute Error (MAE), and Root Mean Squared Error (RMSE), and providing insights into when to use each.

Mean Squared Error (MSE), Mean Absolute Error (MAE), and Root Mean Squared Error (RMSE) are commonly used regression error metrics that help assess the performance of a regression model by quantifying the difference between predicted and actual values. Here’s a detailed explanation of each metric:

Mean Squared Error (MSE):

Formula:

• MSE = 1/n ​∑​(yi​ − y^​i​)²
• n is the number of data points.
• yi​ is the actual value.
• y^​i​ is the predicted value.
• Squaring the errors emphasizes larger errors more than smaller ones.

Key Points:

• MSE penalizes larger errors more heavily than smaller errors due to the squaring operation.
• It is sensitive to outliers because of the squaring effect.
• Commonly used in situations where larger errors are considered more critical.

Mean Absolute Error (MAE):

Formula:

• MAE = 1/n ​∑ ​∣yi​−y^​i​∣
• n is the number of data points.
• yi​ is the actual value.
• y^​i​ is the predicted value.
• Absolute values are used, making MAE less sensitive to outliers compared to MSE.

Key Points:

• MAE is less sensitive to outliers compared to MSE because it doesn’t square the errors.
• Provides a more balanced view of the model’s performance across the entire range of predictions.
• Useful when all errors, regardless of size, are equally important.

Root Mean Squared Error (RMSE):

Formula:

• RMSE = √ 1/n ​∑ (yi​−y^​i​)²​
• n is the number of data points.
• yi​ is the actual…