The Angle Between Two Data Vectors Is Extremely Telling

The angle between two data vectors is extremely telling. And in fact, you could see it in your data matrix if you converted everything to z scores. If two things correlated one point zero, the columns of z scores would be identical. So that's why when you draw that vector out there when it's standardized, you're drawing the exact same vector whether it's standardized x one or standardized x two. When they fall at right angles to each other are really just like the axis that defines al and beth and karl because those people are independent.