# Geometrical interpretation of correlation of a variable and the residual

I came across this blog post about least angle regression, and at a point he says:

• Find the variable $$x_1$$ most correlated with the residual. (Note that the variable most correlated with the residual is equivalently the one that makes the least angle with the residual, whence the name.)

• Move in the direction of this variable until some other variable $$x_2$$ is just as correlated.

But I couldn't visualize it. By "residual" he is referring to the vectors minus the average of the vectors, am I right? What could be a geometrical interpretation of "variable correlation with the residual"? What would be a, let's say, 2D example of this interpretation?

• stats.stackexchange.com/a/1448
– whuber
Commented Jun 12, 2012 at 16:40
• see also "13 ways to look at the correlation coefficient" by Rodgers and Nicewander: data.psych.udel.edu/laurenceau/… Commented Jun 12, 2012 at 17:05
• The original LARS paper has several illustrative figures of the procedure. Have you also looked there? The linked blog post has an adapted version of one of them. Commented Jun 12, 2012 at 17:06
• No pictures, but related: stats.stackexchange.com/questions/6795/… Commented Jun 12, 2012 at 17:09
• @shabby: this article is incredible! I really love this kind of reasoning, multiple point of views in the same concept... Fantastic! Commented Jun 13, 2012 at 3:01