How to fit a curve using "power" fitting or "custom fitting"?

I have data which I need to fit using following equation:

y= f(x)= a*x^b+c.

Code:

r=scatter(npp7,lk_2k1);

r.MarkerEdgeColor = 'r';

r.MarkerFaceColor = [0.9 0.9 0.9];

hold on

% Power fit - %y=f(x)=a*x^b+c

a=28.54;

b=0.4634

c=-3.289;

x = data(:);

y = a*x^b+c;

%f = fit(x,y);

p = plot(x,y)

p(1).LineWidth = 2;

c = p.Color;

p.Color = 'r';

It shows: Error using ^ One argument must be a square matrix and the other must be a scalar. Use POWER (.^) for elementwise power.

But if I use(.^), it shows multiple fit lines as shown in attached figure. I want just one fit line for same equation.

Answer 1

[Image Analyst]

I attach a demo to do an exponential fit. Adapt as needed.

[ishita agrawal]

Thank you.

[Image Analyst]

Below is the full demo:

% Uses fitnlm() to fit a non-linear model (a power law curve) through noisy data.
% Requires the Statistics and Machine Learning Toolbox, which is where fitnlm() is contained.
% Initialization steps.
clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 20;

% Create the X coordinates: 30 points from 0.01 to 20, inclusive.
X = linspace(0.01, 20, 30);

% Define function that the X values obey.
a = 10 % Arbitrary sample values I picked.
b = 0.4
c = 2
Y = a * X .^ b + c; % Get a vector.  No noise in this Y yet.

% Add noise to Y.
Y = Y + 0.8 * randn(1, length(Y));
% Now we have noisy training data that we can send to fitnlm().
% Plot the noisy initial data.
plot(X, Y, 'b*', 'LineWidth', 2, 'MarkerSize', 15);
grid on;

% Convert X and Y into a table, which is the form fitnlm() likes the input data to be in.
tbl = table(X', Y');
% Define the model as Y = a * (x .^ b) + c
% Note how this "x" of modelfun is related to big X and big Y.
% x((:, 1) is actually X and x(:, 2) is actually Y - the first and second columns of the table.
modelfun = @(b,x) b(1) * x(:, 1) .^ + b(2) + b(3);  
beta0 = [10, .4, 2]; % Guess values to start with.  Just make your best guess.
% Now the next line is where the actual model computation is done.
mdl = fitnlm(tbl, modelfun, beta0);
% Now the model creation is done and the coefficients have been determined.
% YAY!!!!

% Extract the coefficient values from the the model object.
% The actual coefficients are in the "Estimate" column of the "Coefficients" table that's part of the mode.
coefficients = mdl.Coefficients{:, 'Estimate'}
% Create smoothed/regressed data using the model:
yFitted = coefficients(1) * X .^ coefficients(2) + coefficients(3);
% Now we're done and we can plot the smooth model as a red line going through the noisy blue markers.
hold on;
plot(X, yFitted, 'r-', 'LineWidth', 2);
grid on;
title('Power Law Regression with fitnlm()', 'FontSize', fontSize);
xlabel('X', 'FontSize', fontSize);
ylabel('Y', 'FontSize', fontSize);
legendHandle = legend('Noisy Y', 'Fitted Y', 'Location', 'north');
legendHandle.FontSize = 25;

message = sprintf('Coefficients for Y = a * X ^ b + c:\n  a = %8.5f\n  b = %8.5f\n  c = %8.5f',...
coefficients(1), coefficients(2), coefficients(3));
text(8, 15, message, 'FontSize', 23, 'Color', 'r', 'FontWeight', 'bold', 'Interpreter', 'none');
% Set up figure properties:
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0, 0.04, 1, 0.96]);
% Get rid of tool bar and pulldown menus that are along top of figure.
% set(gcf, 'Toolbar', 'none', 'Menu', 'none');
% Give a name to the title bar.
set(gcf, 'Name', 'Demo by ImageAnalyst', 'NumberTitle', 'Off')

If you need more help, attach npp7 and lk_2k1.

[ishita agrawal]

This is good enough. Thank you so much.