Standard Error of Regression Calculator Formula
Understand the math behind the standard error of regression calculator. Each variable explained with a worked example.
Formulas Used
Standard Error of Regression
se_reg = sqrt(sse / (n - p - 1))Mean Squared Error (MSE)
mse = sse / (n - p - 1)Variables
| Variable | Description | Default |
|---|---|---|
sse | Residual Sum of Squares (SSE) | 200 |
n | Sample Size (n) | 50 |
p | Number of Predictors (p) | 2 |
How It Works
Standard Error of Regression (RMSE)
The standard error of regression (also called residual standard error or RMSE) estimates the standard deviation of the residuals.
Formula
Se = sqrt(SSE / (n - p - 1))
where SSE is the sum of squared residuals, n is sample size, and p is the number of predictors. Smaller Se means better prediction accuracy. The denominator (n - p - 1) accounts for the degrees of freedom lost estimating the model parameters.
Worked Example
SSE = 200, n = 50, p = 2 predictors.
- 01df = 50 - 2 - 1 = 47
- 02MSE = 200 / 47 = 4.2553
- 03Se = sqrt(4.2553) = 2.0629
Frequently Asked Questions
How do I interpret the standard error of regression?
It is in the same units as the response variable. Approximately 68% of data points fall within ±1 Se of the regression line, and 95% within ±2 Se. Smaller Se means more precise predictions.
Is Se the same as RMSE?
Nearly. RMSE divides by n, while Se divides by (n-p-1). For large samples, they are practically identical. Se is the unbiased estimator; RMSE from cross-validation is preferred for model selection.
How does Se relate to R²?
They measure complementary aspects: R² is the proportion of variance explained (relative measure), Se is the absolute prediction error (in original units). A model can have high R² but large Se if the total variance is large.
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