Generating an error bar plot with a custom equation fit

I am importing data into my workspace that defines variables x and y and an assocated standard deviation in y

I can plot with error bars representing the latter and i can also fit the data to a custom equation usign cftools

Is it possible to do both ie generate a plot with error bars representing the y data standard deviations and also the fit?

Is the only workaround to plot both the data and the equation?

The code i am using is:

x=Table{:,2} % curly arrows needed to pull variables from a table

y=Table{:,7} % the excel column that is the mean of the readings

% Assign a variable Dev to a table column (the standard deviation column)

dev=Table{:,8}

errorbar(x,y,dev,"-s","MarkerSize",10, "MarkerEdgeColor","red","MarkerFaceColor",[0.65 0.85 0.90], 'CapSize',18) % capsize specifies the size of the horizontal caps on the error bars

xlim([-300 6000])

xlabel('Cell Count')

ylabel('Response')

The equation that I want to fit is: y = ymax*(K*x)^n/(1+(K*x)^n)

any help hugely appreciated

Answer 1

[VBBV]

If you want to add multiple lines for errorbars i.e. both y data and y data fitted along with their deviations, you can plot them together as shown below

x = 0:4;
% y data from table with std deviation
y = [1 2 3 4 5];
% y data from the fitted equation  
y1 = [2 3 4 5 6];

% Y data whole
y = [y;y1];

% standard deviation for y data from table & fitted equation 
dev = [0.2 0.1 0.3 0.1 0.2;
       0.1 0.3 0.4 0.3 0.1];
errorbar(x,y,dev); grid
xlim([-0.1 4.1])
legend('y-data','y-data (fitted)')

[Jason]

Hi..many thanks. I think you are basically saying the workaround is to generate two sets of y data...that plotted from raw with an SD error bar and that generated directly from an Eqn that i would like to compare the data to.

Its not obvious to me how i generate the SD from the fitted equation?

Many thanks

[VBBV]

The SD of y-data from fitted equation (using polyfit and polyval functions) needs to evaluated and then appended to Y-vector . Later plot the data using errorbar

% x data from table 
x = 1:5;
K = 0.1;  % say 
n = 2.5; % say 
ymax = 10; % say 

% y-data for fitted equation ( use polyfit & polyval functions)
y1 = ymax*(K*x).^n./(1+(K*x).^n)

y1 = 1×5

0.0315 0.1757 0.4698 0.9189 1.5022

dev1 = repmat(std(y1),1,5)

y1 = 1×5

0.5987 0.5987 0.5987 0.5987 0.5987

% Y data whole
% y = [y;y1];

% combined SD of table y-data  & fitted equation y-data 
% dev = [0.2 0.1 0.3 0.1 0.2; dev1]

% errorbar(x,y,dev);

Note that, here i have used constant (fixed) x-data points for fitted equation. You can use variable x-data points (with fixed range limits) for fitted equation to generate different SD values that match length of SD obtained from table y-data. one way to obtain it is by doing

x = randi([x_min x_max],1,length(y)); % length(y) from table 
% x_min & x_max are range limits for x- data from table 

[Jason]

Hi, having played arounf with polyfit and polyval my current interpretation is:

1. polyfit generates coefficients for a polynomial fit at a specified order
2. polyval generates an extrapolation through these coefficients ie "the fit"
3. this wont do what i wanted - i dont want to fit data to a simple polynomial but to a specified equation

Am i right?

[VBBV]

3. this wont do what i wanted - i dont want to fit data to a simple polynomial but to a specified equation

For simple polynomial fit you can use fit function as shown and choose a suitable polynomial order for your data

% x data from table 
x = [1:5].';
K = 0.1;  % say 
n = 2.5; % say 
ymax = 10; % say 
% y-data for fitted equation ( use polyfit & polyval functions)
y1 = ymax*(K*x).^n./(1+(K*x).^n)

y1 = 5×1

0.0315 0.1757 0.4698 0.9189 1.5022

% choose a polynomial order for your curve fit 
y1_fit = fit(x,y1,'poly3')

y1_fit = 
     Linear model Poly3:
     y1_fit(x) = p1*x^3 + p2*x^2 + p3*x + p4
     Coefficients (with 95% confidence bounds):
       p1 =   -0.001309  (-0.01181, 0.009191)
       p2 =     0.08558  (-0.009518, 0.1807)
       p3 =     -0.1052  (-0.3614, 0.151)
       p4 =     0.05286  (-0.1431, 0.2489)

h = plot(y1_fit,x,y1,'-o');
h(1).LineWidth = 2;
h(2).LineWidth = 1.5; 
legend('Poly','Fitted Poly Curve')

[Jason]

Hi, many thanks for all this, very much appreciated.

What i actually want to do though is NOT to fit to a polynomial. I want to take any imported y data, plot it and also plot the fit to a specified equation eg to make the y_fit here=ymax*(K*x).^n./(1+(K*x).^n)

Thats what i cant work out how to do

Answer 2

[Jason]

Hugely appreciated thanks. Its the bit in the middle thats key for me...i'll do some digging on polyval

Thank you

[VBBV]

Welcome