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Residual Standard Error Calculator

Calculate residual standard error and what it says about model fit.

About Residual Standard Error Calculator

Residual standard error is the typical prediction error in the response’s own units, which makes it far more interpretable than R-squared. Expressing it relative to the mean gives a scale-free view. A model with high R-squared can still have a residual error too large to be useful, which is why RSE should always be reported alongside it.

Formula

Residual Standard Error

RSE = √(Σresiduals² ÷ (n − p − 1))

RSE
Typical size of a prediction error, in the units of the response
degrees of freedom
Sample size less the parameters estimated

Worked example

With the default values below, Residual Standard Error Calculator returns Residual Standard Error of 9.17663. Change any input above and every figure here is recalculated in your browser.

Inputs used

Sum of squared residualsminimum 0
4,800
Sample sizeminimum 3
60
Number of predictorsaccepts 0–50
2
Mean of the response
120

Results

Residual Standard Error
9.17663
Residual Degrees of Freedom
57
Error Relative to the Mean
7.6472%
Typical 95 Per Cent Prediction Window
35.9717
Rating
Good fit

Step by step

  1. 1Values used
  2. 2Residual Standard Error
  3. 3Residual Standard Error= 9.17663
  4. 4Residual Degrees of Freedom= 57
  5. 5Error Relative to the Mean= 7.6472
  6. 6Typical 95 Per Cent Prediction Window= 35.9717
  7. 7Rating= Good fit

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Residual Standard Error calculated?

RSE = √(Σresiduals² ÷ (n − p − 1)) Residual standard error is the typical prediction error in the response’s own units, which makes it far more interpretable than R-squared. Expressing it relative to the mean gives a scale-free view.

Why does Residual Standard Error matter?

A model with high R-squared can still have a residual error too large to be useful, which is why RSE should always be reported alongside it.

What values do I need to enter?

This calculator takes 4 inputs: Sum of squared residuals, Sample size, Number of predictors, Mean of the response. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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