Explained sum of squares

Explained sum of squares is a way of measuring how much of the total variation (or spread) in a set of numbers is explained by different groups or components. For example, if you have a set of numbers from 1-10, you might wonder why the numbers range from 1-10. If you grouped the numbers as odd numbers (1,3,5,7,9) and even numbers (2,4,6,8,10), then you could use the explained sum of squares to figure out how much of the total range (or spread) of numbers is explained by the groupings. The explained sum of squares would tell you that the groupings explain 80% of the variation in the numbers, while the other 20% is unexplained (or random).