finding a function with 4 variables

2022 10 11
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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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Torsten
Torsten 2022-10-11
What kind of function f do you think is appropriate ?
esti liberman
esti liberman 2022-10-11
I honestly have no idea, lets say somthing with x^2,y^2,z^2
Sam Chak
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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Torsten
Torsten 2022-10-11

1 个投票

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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esti liberman
esti liberman 2022-10-11
thank you!, ill give this a go
esti liberman
esti liberman 2022-10-11
I tried this, this is my code:
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 = [ones(numel(RisingHeightCm),1),mLSugar,mLYeast,mLFlour]\RisingHeightCm;
a = sol(1);
b = sol(2);
c = sol(3);
d = sol(4);
but I get the error "Dimensions of arrays being concatenated are not consistent.", all the vectors are 1X31
Torsten
Torsten 2022-10-11
编辑：Torsten 2022-10-11
Ran in:
Ran in:
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
Sam Chak
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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