How to linearly fit a semilog graph

Hello

I have my data file which is attached below. I have to plot this as semilog ( log scale on Y-axis) and have to linearly fit like the image attached. Please help me with the same

Answer 1

[Jonas]

https://nl.mathworks.com/matlabcentral/answers/163349-linear-fit-of-a-semilog-graph?s_tid=answers_rc1-1_p1_MLT

https://nl.mathworks.com/matlabcentral/answers/78694-linear-regression-on-a-semi-log-scale?s_tid=answers_rc1-3_p3_MLT

[Sonia Goyal]

Thank you for your rresponse. But this isn't working for this data.

Answer 2

[Star Strider]

Try this:

D1 = readmatrix('Data.xlsx');

x = D1(:,1);
y = D1(:,2);
[ymax,idx] = max(y);
idxrng = idx:numel(y);

objfcn = @(b,x,minlim) b(1).*exp(b(2).*x) + minlim;

B = fminsearch(@(b) norm(y(idxrng) - objfcn(b,x(idxrng),y(end))), [ymax; rand]);

figure
plot(x, y)
hold on
plot(x(idxrng), objfcn(B,x(idxrng),y(end)), '-r', 'LineWidth',1.5)
hold off
grid
set(gca, 'YScale','log')

It’s not easy to fit those data.

Using:

idxrng = 1:numel(y);
objfcn = @(b,x,minlim) b(1).*x.*exp(b(2).*x) + minlim;

instead, might be more accurate.

[Sonia Goyal]

Thanks for your response but i will have to linearly fit the above mentioned data and i don't have to linearly fit the whole data. for example, In the picture attached above, data between the range of (5-25 second) was fitted linealy. Also, In my case, the data has to be fitted linearly between 11-40 second.

[Star Strider]

I’m not certain what you want. Note that the ‘11 to 40’ constraint was not previosly mentioned.

An exponential fit is appropriate here because it deals realistically with the additive noise. Doing a linear fit on logarithmically-transformed data is not appropriate, since it violates a number of assumptions of the least-squares method. (I will not post code that I know to be in error.)

Try this:

D1 = readmatrix('Data.xlsx');

xr = D1(:,1);
yr = D1(:,2);
idxrng = (xr >= 11) & (xr <= 40);                                   % Use Only 11 - 40 sec
x = xr(idxrng);                                                     % Use Only 11 - 40 sec
y = yr(idxrng);                                                     % Use Only 11 - 40 sec
[ymax,idx] = max(y);

objfcn = @(b,x) b(1).*x.*exp(b(2).*x) + b(3);

B = fminsearch(@(b) norm(y - objfcn(b,x)), [ymax; rand; y(end)]);

figure
plot(x, y)
hold on
plot(x, objfcn(B,x), '-r', 'LineWidth',1.5)
hold off
grid
set(gca, 'YScale','log')
text(25, 0.0015, sprintf('slope = $%9.6f$\nintercept = $%9.6f$', B([2 1])), 'Interpreter','latex')

.

[Sonia Goyal]

Thank you for you response.

[Star Strider]

My pleasure.