Statistical Variance: Understanding SS Total, SST, and SSE

What is the relationship between SS total, SST, and SSE?

SS total = SST + SSE

Answer:

SST (Sum of Squares Total) represents the total variance in the observed data. SSE (Sum of Squared Errors) measures the unexplained variance. The total variance (SS total) in the data is expressed as the sum of the two, i.e., SS total = SST + SSE.

In statistics, SS total, SST, and SSE are all related in terms of variation in data. SST stands for Sum of Squares Total, representing the total variance in the observed data. On the other hand, SSE represents the Sum of Squared Errors, measuring the unexplained variance or the variation within the samples due to chance.

The relationship between these terms can be illustrated through the equation: SS total = SST + SSE. This equation shows how the total variance in the data is divided into two parts—the variance that can be explained by the independent variable(s) (SST) and the variance that is error or unexplained (SSE).

Analogously, think of SS total as a whole pizza. SST would be a portion of the pizza that is explained by the regression model, while SSE is the remaining portion that the model fails to explain. This fundamental equation is essential in the Analysis of Variance (ANOVA) in statistical modelling.