How do you solve the non-growth rate of yeast using non-linear regression analysis?

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clc
clear all
format long

x = [2 1 0.666666667 0.5 0.4 0.33333 0.285714 0.25 0.22222 0.2];
y = [4.4661998 3.09281539 2.685948193 2.784406211 3.011748832 3.591154269 4.108564714 4.306224216 5.041999859 5.766547107 ];
%data values
p = polyfit(x,y,3)
kk= polyval(p,x)
plot(x,y,x,kk,'o')

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clc
clear all
format long
N= 50;
aa = [2 1 0.666666667 0.5 0.4 0.33333 0.285714 0.25 0.22222 0.2];
cd = [4.4661998 3.09281539 2.685948193 2.784406211 3.011748832 3.591154269 4.108564714 4.306224216 5.041999859 5.766547107 ];
 %data values
aa_ini = 0; aa_end=2;
aa_vector = linspace(aa_ini, aa_end, N);
cd_ls = interp1(aa, cd, aa_vector);
cd_cs = spline(aa, cd, aa_vector);
cd_aa13_ls = cd_ls(49)
cd_aa13_cs = cd_cs(49)
% Plotting data points and interpolation line
figure(1)
plot(aa, cd,'o'); hold on
plot(aa_vector, cd_ls, '--');
plot(aa_vector, cd_cs);
plot(aa_vector(8), cd_aa13_cs, 'square');
plot(aa_vector(8), cd_aa13_ls, '+');

[John D'Errico]

Please don't edit the question after it has been answered. This makes Answers less valuable to others. It insults alan who spent the time to answer your question, in that now his answers is less valuable to othersm whi now have a harder time finding it.

[Rik]

Anyone with editing priviliges can still edit back your original question from the Google cache.

[Matt J]

Anyone with editing priviliges can still edit back your original question from the Google cache.

Yes, here it is:

It is known that the non-growth rate of yeast(k) has the following relationship with the food concentration(x)

k = 𝑎𝑥 /(𝑏 + 𝑐𝑥 + 𝑑𝑥^2 + 𝑒𝑥^3)

According to this equation, due to the limitation of food volume, growth approaches zero at very low concentrations. It also approaches zero at high concentrations due to the effects of toxic effects.

(1) The nonlinear regression analysis of the rough experimental data finds the coefficients a, b, c, d, and e.

(2) Plots the data in the [0 5] area.

(3) Obtain the concentration from k(x) that makes k the maximum.

The answer I wrote for 3 hours is as below.

I tried to get X,k by using the reciprocal.

-----------------------------------------------------------------------

clc

clear all

format long

x = [2 1 0.666666667 0.5 0.4 0.33333 0.285714 0.25 0.22222 0.2];

y = [4.4661998 3.09281539 2.685948193 2.784406211 3.011748832 3.591154269 4.108564714 4.306224216 5.041999859 5.766547107 ];

%data values

p = polyfit(x,y,3)

kk= polyval(p,x)

plot(x,y,x,kk,'o')

------------------------------------------------------------------------------

clc

clear all

format long

N= 50;

aa = [2 1 0.666666667 0.5 0.4 0.33333 0.285714 0.25 0.22222 0.2];

cd = [4.4661998 3.09281539 2.685948193 2.784406211 3.011748832 3.591154269 4.108564714 4.306224216 5.041999859 5.766547107 ];

%data values

aa_ini = 0; aa_end=2;

aa_vector = linspace(aa_ini, aa_end, N);

cd_ls = interp1(aa, cd, aa_vector);

cd_cs = spline(aa, cd, aa_vector);

cd_aa13_ls = cd_ls(49)

cd_aa13_cs = cd_cs(49)

% Plotting data points and interpolation line

figure(1)

plot(aa, cd,'o'); hold on

plot(aa_vector, cd_ls, '--');

plot(aa_vector, cd_cs);

plot(aa_vector(8), cd_aa13_cs, 'square');

plot(aa_vector(8), cd_aa13_ls, '+');

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You can untie it with the top. Isn't it impossible to get a coefficient?

[pp1459]

oh sorry.... a

Answer 1

[Alan Stevens]

You can do it as follows. Notice that there are, in effect, only four paramters to fit:

x = 0:0.5:5;   % mg/L
k = [0, 0.223904, 0.323333, 0.372308, 0.359143, 0.332033, 0.278462, ...
     0.243394, 0.232222, 0.198334, 0.173414];    % d^-1
 
% In the following function r(1) = b/a, r(2) = c/a, r(3) = d/a, r(4) = e/a
 f = @(x, r) x./(r(1) + r(2)*x + r(3)*x.^2 + r(4)*x.^3); 
 
 r0 = ones(4,1);
 r = fminsearch(@(r) fcn(r,x,k,f),r0);
 
 xx = 0:0.01:5;
 kfit = f(xx,r);
 
 plot(x,k,'o',xx,kfit),grid
 xlabel('x'),ylabel('k')
 legend('data','curvefit')
 
 function F = fcn(r,x,k,f)
 
          y = f(x,r);
          F = norm(y-k);
 end

This results in the following

[pp1459]

thank you ,sir ㅠㅠㅠ thanks!!!!!