However, S must be <= 2.5 to produce a sufficiently narrow 95% prediction interval. Is the R-squared high enough to achieve this level of precision? There’s no way of knowing. Suppose our requirement is that the predictions must be within +/- 5% of the actual value. The regression model produces an R-squared of 76.1% and S is 3.53399% body fat. To illustrate this, let’s go back to the BMI example. However, you can’t use R-squared to assess the precision, which ultimately leaves it unhelpful. Further, as I detailed here, R-squared is relevant mainly when you need precise predictions. And, if I need precise predictions, I can quickly check S to assess the precision.Ĭonversely, the unit-less R-squared doesn’t provide an intuitive feel for how close the predicted values are to the observed values. I love the practical, intuitiveness of using the natural units of the response variable.
In many cases, I prefer the standard error of the regression over R-squared. Why I Like the Standard Error of the Regression (S) 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.įor the BMI example, about 95% of the observations should fall within plus/minus 7% of the fitted line, which is a close match for the prediction interval. Unlike R-squared, you can use the standard error of the regression to assess the precision of the predictions. S is 3.53399, which tells us that the average distance of the data points from the fitted line is about 3.5% body fat. The fitted line plot shown above is from my post where I use BMI to predict body fat percentage. Smaller values are better because it indicates that the observations are closer to the fitted line. Conveniently, it tells you how wrong the regression model is on average using the units of the response variable. S represents the average distance that the observed values fall from the regression line.
S is known both as the standard error of the regression and as the standard error of the estimate. Both statistics provide an overall measure of how well the model fits the data. In the regression output for Minitab statistical software, you can find S in the Summary of Model section, right next to R-squared. S becomes smaller when the data points are closer to the line.
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