finding a function with 4 variables

Question

esti liberman 2022-10-11

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https://ww2.mathworks.cn/matlabcentral/answers/1822218-finding-a-function-with-4-variables

编辑： Sam Chak 2022-10-11

Hello, for a project im doing I measured the hight of rising dough as im playing with 3 variables (flour sugar yeast). and so I ended up having 4 vectors.

how can I fit a function to this data? (i.e hegiht =f(sugar,yeast,flour))

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Ghazwan 2022-10-11

This post will give more ideas

https://www.mathworks.com/matlabcentral/answers/15584-is-it-possible-to-have-3-or-more-variable-inputs-for-a-3d-contour-plot-in-gui

Sam Chak 2022-10-11

Since you have collected the data, maybe the batch least squares estimation?

You can find mre info here:

https://www.mathworks.com/help/curvefit/least-squares-fitting.html

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Answer 1

Torsten 2022-10-11

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https://ww2.mathworks.cn/matlabcentral/answers/1822218-finding-a-function-with-4-variables#answer_1071323

在 MATLAB Online 中打开

I suggest you start with

height = a + b * sugar + c * yeast + d * flour

If height,sugar, yeast and flour are column vectors of equal length, this would give the code

sol = [ones(numel(height),1),sugar,yeast,flour]\height
a = sol(1)
b = sol(2)
c = sol(3)
d = sol(4)

for the regression coefficients a, b, c and d.

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Torsten 2022-10-11

编辑：Torsten 2022-10-11

在 MATLAB Online 中打开

I wrote column vectors, not row vectors.

numOfExp = 1:31;
mLFlour = [15,15,15,15,15,15,15,22.5,22.5,22.5,22.5,22.5,22.5,30,30,30,30,30,30,37.5,37.5,37.5,37.5,45,45,45,52.5,52.5,52.5,60,60].';
mLYeast = [7.5,15,22.5,30,37.5,45,52.5,7.5,15,22.5,30,37.5,45,7.5,15,22.5,30,37.5,45,7.5,15,22.5,30,7.5,15,22.5,22.5,15,7.5,7.5,15].';
mLSugar = [52.5,45,37.5,30,22.5,15,7.5,45,37.5,30,22.5,15,7.5,37.5,30,22.5,15,7.5,0,30,22.5,15,7.5,22.5,15,7.5,0,7.5,15,7.5,0].';
RisingHeightCm = [3,3.5,4.3,4.1,7.9,5.9,4,3.1,2.6,3.2,7.1,7.9,4.9,2.5,2.6,5,8,3.9,4.3,2.8,4.5,10.6,4.5,2.6,5.6,3.7,4.2,5.7,6,5.6,4.5].';
BakingHeightCm = [3.9,6,6.6,6.5,5.7,5.9,3.4,4.9,5.5,5.8,9.4,5.6,4.7,4,5.5,7.6,9.5,3.8,4,5.4,7.1,4.8,4.6,5.6,8.7,4.3,4.1,5.5,7.9,6.8,4.6].';
sol = [mLSugar,mLYeast,mLFlour]\RisingHeightCm;
a = sol(1)
a = 0.0270
b = sol(2)
b = 0.0948
c = sol(3)
c = 0.0646
error = [mLSugar,mLYeast,mLFlour]*sol - RisingHeightCm
error = 31×1
    0.1000
    0.1086
   -0.1829
    0.5257
   -2.7657
   -0.2571
    2.1514
    0.2819
    1.2905
    1.1990

esti liberman 2022-10-11

Thank you!

Sam Chak 2022-10-11

编辑：Sam Chak 2022-10-11

Hi @esti liberman

I remember making dough.

Did you miss Salt and Warm Water as parts of the ingredients?

The temperature of the water is also sort of important. If it is too hot, then it will kill the yeast.

I think yeast is a kind of fungus.

By the way, does the baker's mixing skill influence the rising height of the dough?

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finding a function with 4 variables

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