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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?

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    $\begingroup$ Why would that be 200-dimensional? If you have two variables, your problem is 2-dimensional. That doesn't change, whether you have $1$, $2$, $200$, or $1,000,000$ observations of $\{X, Y\}$. The observations are points in the 2-dimensional space. $\endgroup$ – Frans Rodenburg Sep 30 '19 at 6:34
  • $\begingroup$ So the space we are working in 200 dimensional space, as each of the vectors i.e. X & Y is a vector in 200 D. The sub-space we are working is 2 dimensional. $\endgroup$ – Sameer Saurabh Sep 30 '19 at 6:40
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No, you don't have two vectors in 200 dimensional space, you have 200 vectors (or ordered pairs) in a 2 dimensional space. Those two dimensions are X and Y.

If you really have two vectors in a 200 dimensional space, then a scatter plot would not be a good graph. Probably no graph would be good as it would only have two points and there is no way to show a 200 dimenisonal space.'

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  • $\begingroup$ On the contrary, the OP indeed does have a pair of $200$-vectors. That's a mathematical fact. The issue is that these data have multiple valid interpretations. $\endgroup$ – whuber♦ Oct 1 '19 at 1:35

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