Final answer:
The standard error of the estimate indicates the accuracy of the regression predictions and is calculated as the square root of the Sum of Squared Errors (SSE) divided by the degrees of freedom, subsequently finding the standard deviation of the residuals.
Step-by-step explanation:
The standard error of the estimate, denoted se, is a measure of the accuracy of predictions made with a regression line. It represents the standard deviation of the residuals (the vertical distances between actual Y values and the predicted values from the regression line). The standard error of the estimate is computed by taking the square root of the average squared differences, this quantity is known as the Sum of Squared Errors (SSE).
Mathematically, the SSE is the sum of the squared differences between each actual Y value and its corresponding predicted value on the regression line, denoted as ε-values or residuals. The formula for se is derived from the SSE by dividing it by the degrees of freedom (typically n - 2 where n is the number of data points) and then taking the square root of this value to calculate the standard deviation of the residuals.