Method for experimental results analysis

[miraboreasu]

Hello guys, I have conducted an experiment and got some results.
I have 3 variables to vary, for example, five x1, five x2, and two x3
and 2 observation results, like y1, y2
I already make y1 y2 and x1 x2 x3 dimensionless
since plot is 2D, what I am doing now is just plot when x3=1, x2=1, plot the first y1(x1), x3=1, x2=2, plot the second y1(x1), etc
the same plots for y2

I want to know if is there a better way to analyze the results, for example, what method I should learn to create a function y1=(x1,x2,x3)?

 

[Baluncore]

Analysis will depend on what mathematical relationship you are expecting. Once you nominate the possible functions and parameters, you can solve for those parameters using a least squares fit.

 

[miraboreasu]

Analysis will depend on what mathematical relationship you are expecting. Once you nominate the possible functions and parameters, you can solve for those parameters using a least squares fit.

Thanks, sir, but I didn't quite understand, I have multi varying, and I want to create a unified function for them.

What I am thinking is y1= alpha x1+beta x1+gamma x1. But I want to know more details

 

[Baluncore]

y₁ = a·x₁ + b·x₂ + c·x₃ ; you must find the parameters a, b and c.
If you believe the relationship is linear, then you might solve a set of linear equations by numerically inverting a matrix.
https://en.wikipedia.org/wiki/Linear_algebra
https://en.wikipedia.org/wiki/Numerical_linear_algebra

 

[Tom.G]

I'm not real sure what your desired end result is, but if you are trying to get 3 variables and 1 or 2 results on a single graph, here is one approach:

1) A surface represented as a 3D graph with a variable on each axis
2) the dependent variable(s) (y1, y2) as the color of the surface
3) the color could be a mix to show the various mixes of y1, y2; or maybe color and texture... hmm... even shading lines, say density or line width in one axis for y1 and in a cross direction for y2.

A 3D bar graph is another possible representation which may be better if you need to print the result, rather than interactively display it on-screen.

It has been decades, but I seem to recall that programs like Microsoft Office can show 3D graphs. Of course there are many free Office-type programs now available.

Please let us know what you come up with. We like to learn too!

Cheers,
Tom