Rms Error Calculator

Enter the observed and predicted values into the calculator to determine the Root Mean Square (RMS) Error. The values should be comma-separated.

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RMS Error Formula

The following formula is used to calculate the RMS Error:

RMS Error = √(Σ(observed - predicted)² / n)

Variables:

• observed - The actual observed values.
• predicted - The predicted values based on a model.
• n - The number of observations or predictions.

To calculate the RMS Error, take the square root of the average of the squares of the differences between observed and predicted values.

What is RMS Error?

RMS Error is a measure used to evaluate the differences between values predicted by a model or an estimator and the actual values observed. The RMS Error represents the square root of the second sample moment of the differences between predicted values and observed values or the quadratic mean of these differences. It is commonly used in forecasting and regression analysis to verify experimental results.

How to Calculate RMS Error?

The following steps outline how to calculate the RMS Error:

1. First, list the observed values and the predicted values.
2. Ensure that the number of observed values matches the number of predicted values.
3. Calculate the difference between each observed value and its corresponding predicted value, then square the result.
4. Sum all the squared differences.
5. Divide the sum of the squared differences by the number of observations (n).
6. Take the square root of the result to get the RMS Error.
7. Use the calculator above to check your calculations.

Example Problem:

Use the following variables as an example problem to test your knowledge.

Observed values: 3, 5, 6, 7

Predicted values: 2.5, 4.8, 6.1, 7.2