finding a function with 4 variables

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))

[Torsten]

What kind of function f do you think is appropriate ?

[esti liberman]

I honestly have no idea, lets say somthing with x^2,y^2,z^2

[Ghazwan]

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]

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

Answer 1

[Torsten]

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.

[esti liberman]

thank you!, ill give this a go

[esti liberman]

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]

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]

Thank you!

[Sam Chak]

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?