#Standard error online statbook how to

Roughly 95% of the observation should fall within +/- two standard error of the regression, which is a quick approximation of a 95% prediction interval. The standard error of the regression is particularly useful because it can be used to assess the precision of predictions. But on average, the observed values fall 4.19 units from the regression line. Notice that some observations fall very close to the regression line, while others are not quite as close. If we plot the actual data points along with the regression line, we can see this more clearly:

In this case, the observed values fall an average of 4.89 units from the regression line. The standard error of the regression is the average distance that the observed values fall from the regression line. In this case, 65.76% of the variance in the exam scores can be explained by the number of hours spent studying. R-squared is the proportion of the variance in the response variable that can be explained by the predictor variable. If we fit a simple linear regression model to this dataset in Excel, we receive the following output: Suppose we have a simple dataset that shows how many hours 12 students studied per day for a month leading up to an important exam along with their exam score:

#Standard error online statbook how to

This tutorial explains how to interpret the standard error of the regression (S) as well as why it may provide more useful information than R 2.

Two metrics commonly used to measure goodness-of-fit include R-squared (R 2) and the standard error of the regression, often denoted S. When we fit a regression model to a dataset, we’re often interested in how well the regression model “fits” the dataset.