Standard error of regression Biostatistics and Research Methodology Notes
The standard error of the regression (S), also known as the standard error of the estimate, represents the average distance that the observed values fall from the regression line. Conveniently, it tells you how wrong the regression model is on average using the units of the response variable. Smaller values are better because it indicates that the observations are closer to the fitted line.
Unlike R-squared, you can use the standard error of the regression to assess the precision of the predictions. Approximately 95% of the observations should fall within plus/minus 2*standard error of the regression from the regression line, which is also a quick approximation of a 95% prediction interval. If want to use a regression model to make predictions, assessing the standard error of the regression might be more important than assessing R-squared.
The Advantages of Using the Standard Error
The standard error of the regression (S) is often more useful to know than the R-squared of the model because it provides us with actual units. If we’re interested in using a regression model to produce predictions, S can tell us very easily if a model is precise enough to use for prediction.