Error sum of squares \(\rm (S_E^2)\) is calculated by: 

Key Points 

The Error Sum of Squares (SSE) is a measure of the amount of variability in the data that is not explained by the statistical model. It is often used in the context of regression analysis or ANOVA (Analysis of Variance). However, the formula you provided seems to correspond to the calculation of the "within-group" sum of squares for a one-way ANOVA, rather than the error sum of squares. In the context of a one-way ANOVA, where we are comparing means of different groups: 

• y_ij represents the j^th observation in the ith group.
• \(\bar{y}_i\) represents the mean of the ith group. 

The "within-group" sum of squares (which is analogous to the Error Sum of Squares in this context) is then calculated as: \(\rm \Sigma_i \Sigma_j (y_{ij}-\bar y_{i.})^2\)

This calculates the squared deviations of each observation from their respective group means and then sums all these squared deviations. This gives a measure of the variability within each of the groups.
However, in a more general context (like a regression analysis), the Error Sum of Squares is calculated as the sum of the squared deviations of the observed values from the values predicted by the model.
In this case, it y_i is the observed value and \(\hat{y}_i\) is the value predicted by the model for the ith observation, the Error Sum of Squares (SSE) would be: \(SSE = \Sigma_i(y_i - \hat{y}_i)^2\)
This calculates the squared deviations of each observation from its predicted value and then sums all these squared deviations. This gives a measure of the variability in the data that is not explained by the model.