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Root Mean Squared Error (RMSE) is a commonly used metric to evaluate the performance of a regression model. It provides a measure of how well the model's predictions match the actual values in the dataset. The RMSE is calculated by taking the square root of the average of the squared differences between the predicted and actual values.
The formula for calculating RMSE is:
RMSE = sqrt(Σ(y_pred - y_true)^2 / n)
Where:
The RMSE value is a measure of the average deviation between the predicted values and the actual values. A lower RMSE value indicates that the model is better at predicting the target variable, while a higher RMSE value indicates a larger deviation between the predicted and actual values.
RMSE is measured in the same units as the target variable, which makes it easy to interpret. For example, if the target variable is in dollars, then the RMSE will also be in dollars.
Here is a step-by-step guide on how to calculate RMSE:
Let's consider a simple example to illustrate how RMSE is calculated:
Actual Value | Predicted Value | (Predicted - Actual)^2 |
---|---|---|
10 | 12 | (12 - 10)^2 = 4 |
20 | 18 | (18 - 20)^2 = 4 |
30 | 28 | (28 - 30)^2 = 4 |
Now, we calculate the RMSE:
RMSE = sqrt((4 + 4 + 4) / 3) = sqrt(4) = 2
Therefore, the RMSE in this example is 2.
RMSE is widely used in various fields and applications, including:
There are several advantages of using RMSE as an evaluation metric: