202602132203
Status: #reference
Tags: Statistics, Residual Sum of Squares (RSS)
State: #nascient

Sum of Squares

The concept of sum of squares is quite a useful one used everywhere in statistics. When used it almost invariably refers to an error or deviation of some form. The reason why is it so common is because of its convenient properties.

1. By summing squares, we prevent deviations/errors from cancelling each other.
2. A sum of squares is easily differentiable using standard calculus, other means of computing deviation like Sum of Absolute Values are non-trivial to differentiate and in fact were not really tractable until modern computing made computing Sub-Gradients more or less trivial.
3. Even today where absolute values are easy to differentiate, a strong body of mathematical literature makes deriving many results easier.

One of the most important uses of the sum of squares is in the context of Analysis of Variance (ANOVA) where by dividing sum of squares by their degrees of freedom we obtain sample statistics which we can show follow a Chi-Squared Distribution with the degrees of freedom.

Finally, by taking the ratio of independent Chi-Squared Distribution we obtain the Fisher Distribution.

Relevant Links