Math: 3-variable statistics

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harry ravi
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Math: 3-variable statistics




by harry ravi » 12/09/08, 19:10

Hello everyone,

here I am not a light in maths, I wanted to know if there is a formula to determine a linear fit on a point cloud of a statistical study with 3 variables.

If so, could you give me the formula?

Thank you in advance.
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by Christophe » 12/09/08, 19:12

A 3D barycenter?
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harry ravi
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by harry ravi » 12/09/08, 19:14

To your wishes, I don't know what to talk about.
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by Christophe » 12/09/08, 19:24

Well all the same for me! : Cheesy:
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harry ravi
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by harry ravi » 12/09/08, 19:45

I take the case of a statistic with 2 variables Xi and Ni with n points in the cloud.

The linear fit line is an affine function of the form:
Ni = aXi + b


We have:
mXi = average of the points Xi
mNi = average of Ni points
€ XiNi = sum of the products XiNi
€ Xi² = sum of Xi²
€ Ni² = sum of Ni²

We obtain a the directing coefficient of the linear adjustment line by:
a = (€ XiNi - n mXi mNi) / (€ Xi² - n (mXi) ²)

we obey b by the following formula:
b = mNi - a mXi


In addition, it is possible to check whether there is a functional link between the two parameters by determining the linear correlation coefficient.
This can only be between -1 and 1.
If it is close to 1 (eg 0,87) there is a possible linear correlation therefore a link between the parameters.

It is calculated as follows:

r = aa '

with a the previous formula and a ':

a '= a = (€ XiNi - n mXi mNi) / (€ Ni² - n (mNi) ²)


So I wanted to know if we could get a correlation calculation in a 3-variable statistic.
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by Remundo » 14/09/08, 11:36

Hi Harry,

Does your three-dimensional point cloud is grouped around a line (in the space).

If not, there is no way it will work.

If so, I see 2 solutions:
- make a projection in the plane and find 3 directing coefficients: 1 in the xy plane, 1 in the yz plane, 1 in the xz plane: you can reuse the classical linear regression formulas in the plane. By the way, you find the y-intercepts x0, y0, z0
- try to tweak the formulas to directly find the directing cosines of a collinear vector on your right (3 coefficient) + the y-intercept ... I admit that I never thought about the question, but if a mathematician wants to stick to it : Cheesy:

If you want to go fast, I recommend the first method ... : Idea:
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harry ravi
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by harry ravi » 14/09/08, 11:48

I don't have a point cloud yet because I don't have any variables to apply.


I was thinking about that in case it helps.

I may need it later.

Goods.
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