I'm looking for a mathematical description of a data-set, but i have trouble finding the right wording. So i will just describe the situation.
I have a data-set where each data-point consists of a values for three (interval) variables. So <x=1.2, y=24, z=12> would be a data-point.
When i plot the joint density distribution (using kernel smoothing) of two of the variables, i get a ellipse shaped mountain, whose axis runs parallel with to a line described by y = a - bx.
When i plot the data-points in 3D with each variable on it's own axis, i get something resembling a wedge.
None of this is surprising, as the general shape of the dependecies is known beforehand.
But i want to come up with a mathematical description, describing the third variable in terms of the other two.
More precicely, i'm interested in when the third variable passes over a threshold.
Also, I have an idea what this function should look like. I want to draw a series of paralel lines that denote density boundries. So there will be a 50% line, meaning: 'of the data-points whose coordinates (the first two variables) fall left of this line, 50% will have higher than threshold for the third variable.'
And another parallel line for 'of the data-points whose coordinates (the first two variables) fall left of this line, 90% will have higher than threshold for the third variable.' and so on.
How do i go about doing this? I'm not even sure of the terminology, this makes it hard to ask the right questions.
Thanks!
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