## Orthogonality in mathematics

The word Orthogonality originates from a combination of two words in ancient Greek: orthos (upright), and gonia (angle). It has a geometrical meaning. It means two lines create a 90 degrees angle between them. So one line is perpendicular to the other line. Like so:

Even though Orthogonality is a geometrical term, it appears very often in statistics. You probably know that in a statistical context

*orthogonality*means uncorrelated, or linearly independent. But why?

Why use a geometrical term to describe a statistical relation between random variables? By extension, why does the word *angle* appears in the incredibly common regression method least-angle regression (LARS)? Enough losing sleep over it (as you undoubtedly do), an extensive answer below.