Enter the sum of squared residuals, sample size, and number of predictors into the calculator to determine the standard error of regression. This calculator helps in assessing the accuracy of the predictions made by a regression model.

Standard Error of Regression Formula

The following formula is used to calculate the standard error of regression (SER): 

SER = √(SSR / (n - p - 1))

Variables:

  • SSR is the sum of squared residuals
  • n is the sample size
  • p is the number of predictors in the regression model

To calculate the standard error of regression, take the square root of the sum of squared residuals divided by the degrees of freedom (n – p – 1).

What is Standard Error of Regression?

The standard error of regression (SER) is a measure that indicates the typical distance that the observed values fall from the regression line. It is an important metric in regression analysis as it gives an estimate of the accuracy of the predictions. A lower SER indicates a better fit of the regression model to the observed data.

How to Calculate Standard Error of Regression?

The following steps outline how to calculate the Standard Error of Regression.

  1. First, determine the sum of squared residuals (SSR).
  2. Next, determine the sample size (n).
  3. Next, determine the number of predictors in the regression model (p).
  4. Next, gather the formula from above = SER = √(SSR / (n – p – 1)).
  5. Finally, calculate the Standard Error of Regression (SER).
  6. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

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

Sum of squared residuals (SSR) = 200

Sample size (n) = 30

Number of predictors (p) = 2