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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(Pi – Oi)2 / n ]


  • Σ is a fancy symbol that means “sum”
  • Pi is the predicted value for the ith observation
  • Oi is the observed value for the ith 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

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