I Method for experimental results analysis

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The discussion centers on analyzing experimental results with three variables (x1, x2, x3) and two outcomes (y1, y2). The user seeks a method to create a unified function for y1 and y2 based on the varying inputs. Suggestions include using a least squares fit to determine parameters for a linear relationship, represented as y1 = a·x1 + b·x2 + c·x3. Additionally, visual representation options such as 3D graphs or surface plots are recommended to effectively display the relationships between the variables and outcomes. The conversation emphasizes the importance of understanding the mathematical relationships to guide the analysis approach.
miraboreasu
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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)?
 
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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.
 
Baluncore said:
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
 
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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
 
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