What is Root Mean Square Error
The Root Mean Square Error (RMSE) is a variant of MSE that calculates the square root of the average squared difference between actual and predicted values. It is often preferred the over MSE as it provides an interpretable measure of the error in the same units as the original data.
RMSE Formula
RMSE = √(MSE)
Examples of Root Mean Square Error
Example: Given the actual and predicted values for the regression problem calculate the MSE and RMSE.
Actual Values: [15, 25, 35, 45, 55]
Predicted Values: [18, 22, 38, 42, 52]
Solution:
The Calculate the squared differences between the actual and predicted values:
Squared Differences: [(15-18)2, (25-22)2, (35-38)2, (45-42)2, (55-52)2]
= [9, 9, 9, 9, 9]
Compute the MSE
MSE = (9 + 9 + 9 + 9 + 9) / 5
= 45 / 5
= 9
Calculate the RMSE:
RMSE = √(9)
= 3
MSE vs RMSE
Mean Squared Error is often compared with the other error metrics such as the Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) to the evaluate model performance. While MAE measures the average absolute difference between predicted and actual values RMSE measures the square root of the average squared difference. The MSE and RMSE penalize large errors more heavily than MAE making them more sensitive to the outliers.
Mean Squared Error
Mean Squared Error (MSE) is a fundamental concept in statistics and machine learning playing a crucial role in the assessing the accuracy of the predictive models. It measures the average squared difference between predicted values and the actual values in the dataset. This article aims to provide a comprehensive overview of the mean squared error, its significance in statistical analysis, and its applications in various domains.