I am stuck in understanding a basic scatter plot. I am working in two dimensions i.e. there are two variables X & Y.
So, the question is that in the scatter plot, what do the two axes mean?
Before answering, please read my confusion below! (I know that we take those axes as X and Y):
I have 200 data points for X & Y. So, I am working in a 200 dimensional space. Now, I have two vectors (each in 200 dimensions) i.e. X & Y. Now these vectors point in some direction in a 200 dimensional space and they are the basis for a 2 dimensional sub space which in this case is a 2-dimensional plane in a 200 dimensional space. Now, it is not necessary that the two vectors X & Y (basis of the 2-D plane) are orthogonal. Ideally, if I find a Eigen vector basis, we might then say that those basis are orthogonal. Then, while making the scatter plot in that 2-d sub space (a plane) why do we take those two axes as X & Y and show them as orthogonal?