Curve fitting for loglog scale

I have fitted a curve using general plot function, now if I want to fit the same data in loglog scale how can I do it.

any help is much appreciated

program:

function [fitresult, gof] = createFit(w, AC1)

%CREATEFIT(W,AC)

% Create a fit.

%

% Data for 'untitled fit 1' fit:

% X Input : w

% Y Output: AC

% Output:

% fitresult : a fit object representing the fit.

% gof : structure with goodness-of fit info.

%

% See also FIT, CFIT, SFIT.

% Auto-generated by MATLAB on 10-May-2022 11:38:11

%% Fit: 'untitled fit 1'.

clc;clear,close all;

opts = spreadsheetImportOptions("NumVariables", 6);

% Specify sheet and range

opts.Sheet = "Sheet1";

opts.DataRange = "A2:F202";

% Specify column names and types

opts.VariableNames = ["f1", "sigmaAcZT1", "f2", "SIGMAACZT2", "F2", "SIGMAACZT3"];

opts.VariableTypes = ["double", "double", "double", "double", "double", "double"];

% Import the data

data = readtable("C:\Users\navaneeth\Downloads\IONIC CONDUCTIVITY.xlsx", opts, "UseExcel", false);

% Convert to output type

data = table2array(data);

% Clear temporary variables

clear opts

f = data(:,1)

w = 2*pi*data(:,1);%w = 2*pi*f

AC1 = data(:,2);%AC conductivity sample 1

AC2 = data(:,4);%AC conductivity sample 2

AC3 = data(:,6);%AC conductivity sample 3

[xData1, yData1] = prepareCurveData( w, AC1 );

[xData2, yData2] = prepareCurveData( w, AC2 );

[xData3, yData3] = prepareCurveData( w, AC3 );

% Set up fittype and options.

ft = fittype( 'power2' );

opts = fitoptions( 'Method', 'NonlinearLeastSquares' );

opts.Algorithm = 'Levenberg-Marquardt';

opts.Display = 'Off';

opts.StartPoint = [9.32271357188677e-06 0.0429375187609614 2.50935751249309e-06];

% Fit model to data.

[fitresult1, gof1] = fit( xData1, yData1, ft, opts );

[fitresult2, gof2] = fit( xData2, yData2, ft, opts );

[fitresult3, gof3] = fit( xData3, yData3, ft, opts );

% Plot fit with data.

figure( 'Name', 'untitled fit 1' );

h = plot(fitresult1,'k',xData1,yData1,'ok');

hold on

g = plot(fitresult2,'k',xData2,yData2,'or');

hold on

f = plot(fitresult3,'k',xData3,yData3,'ob');

legend('ZT-3','fit', 'Location', 'NorthWest')

set(h, 'LineWidth',2)

set(g, 'LineWidth',2)

set(f, 'LineWidth',2)

% Label axes

set(gca,'fontweight','bold','fontsize',16);

xlabel( '\omega');

ylabel('\sigma_{AC} (S/cm)');

fitresult1

fitresult2

fitresult3

grid on

[dpb]

If you're not terribly concerned about the statistics but just a fit, simply log both x and y variables and apply linear fit -- evaluate by logging X then exp() (or 10.^ if use log10) the output to return to original scale.

If need fitting statistics, then fit the nonlinear model.

[Torsten]

Why fitting in loglog scale ? It will introduce bias to the fitting parameters.

[Navaneeth Tejasvi Mysore Nagendra]

Thank you dpb for the suggestion, and for Torsten.

I would like to plot them in loglog scale as my distribution is for power law and it is more appropriate to do so. the problem with that is I am not able to call my fitresults directly inside loglog function. so was wondering if I need to fit for loglog scale data points, how can I do so.

[Torsten]

Plotting in loglog scale is the one thing, fitting is the other. Do the first if you like, don't do the last.

[dpb]

I'll disagree w/ @Torsten that there's never a valid reason for log models; indeed some processes are. The error distribution is mutiplicative rather than additive in this case

As said above, you have two choices -- either

1. log the variables, fit, evaluate y=10.^f(log10X), loglog(X,Y) (because it does the log10 internally), or
2. use nonlinear curve fit and fit the appropriate power model directly. In this case your model will still be in original space; loglog() works as normal for both data and fitted result.