Root Mean Square Error

What is Root Mean Square Error (RMSE)? RMSE Explained

Root Mean Square Error (RMSE) is a commonly used metric for evaluating the performance of a regression model. It measures the average difference between the predicted and actual values of the target variable, taking into account the squared differences.

The RMSE is calculated by taking the square root of the mean of the squared differences between the predicted values (ŷ) and the actual values (y) of the target variable:

RMSE = sqrt(mean((ŷ – y)^2))

Here’s a step-by-step explanation of how to calculate RMSE:

Compute the difference between the predicted values (ŷ) and the actual values (y) of the target variable for each data point.
diff = ŷ – y

Square each difference to eliminate the negative signs and emphasize larger errors.
squared_diff = diff^2

Calculate the mean of the squared differences.
mean_squared_diff = mean(squared_diff)

Take the square root of the mean squared difference to obtain the RMSE.
RMSE = sqrt(mean_squared_diff)

The RMSE provides a measure of the average magnitude of the prediction errors made by the model. It is useful for comparing different models or tuning model parameters. A lower RMSE indicates a better fit between the predicted and actual values, suggesting that the model has better predictive performance.

It is important to note that RMSE is sensitive to outliers because the squared differences magnify larger errors. Therefore, it is advisable to examine other evaluation metrics, such as Mean Absolute Error (MAE), in conjunction with RMSE to gain a comprehensive understanding of the model’s performance.