The **root mean square error (RMSE)** is a metric that tells us how far apart our predicted values are from our observed values in a regression analysis, on average. It is calculated as:

**RMSE** = √[ Σ(P_{i} – O_{i})^{2} / n ]

where:

- Σ is a fancy symbol that means “sum”
- P
_{i}is the predicted value for the i^{th}observation - O
_{i}is the observed value for the i^{th}observation - n is the sample size

To find the RMSE for a regression, simply enter a list of observed values and predicted values in the two boxes below, then click the “Calculate” button:

**Observed values:**

**Predicted values:**

**RMSE** = 2.43242