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

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ishita agrawal on 16 Sep 2017
Commented: ishita agrawal on 22 Sep 2017
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.

Image Analyst on 16 Sep 2017
I attach a demo to do an exponential fit. Adapt as needed.
##### 3 CommentsShow 1 older commentHide 1 older comment
Image Analyst on 16 Sep 2017
Edited: Image Analyst on 16 Sep 2017
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.
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);
% 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 on 22 Sep 2017
This is good enough. Thank you so much.

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