How do I make custom power trendline plots?

I have a question regarding to this answer.

The link is below:

https://kr.mathworks.com/matlabcentral/answers/367835-please-help-me-how-to-fit-the-data-with-a-power-law-function#answer_291921

I want to make a power fitting curve in the form of y=a*x^0.5+c.

However, the linked answer just provide full prediction of the fitting curve including exponent of the curve.

I want to fix the exponent as 0.5 or other value as a constant. Finally, I just want to figure out the number of a and c.

How do I revise the code in this case?

Thank you.

Answer 1

[Star Strider]

Try something like this —

yfcn = @(b,x) b(1).*sqrt(x) + b(2);

x = 0:0.5:10;
y = rand(size(x));

[B,fval] = fminsearch(@(b) norm(y-yfcn(b,x)), rand(2,1))

B = 2×1

0.0233 0.4282

fval = 1.3888

xv = linspace(min(x), max(x));
yv = yfcn(B,xv);

figure
plot(x, y, '.')
hold on
plot(xv, yv, '-r')
hold off
grid
xlabel('X')
ylabel('Y')
title(sprintf('$y(x) = %.3f \\cdot \\sqrt{x} + %.3f$', B), 'Interpreter','latex')

NOTE — Using ‘sqrt(x)’ is computationally more efficient than ‘x.^0.5’.

.

[HyoJae Lee]

It worked!

Sorry but, one more question.

How can I change in case of cube root? (not the square root)

BTW, appreciated for the fast reply!

[Star Strider]

As always, my pleasure!

The cube root would have to be coded as ‘x.^(1/3)’ since I doubt a specific function otherwise exists for it.

[HyoJae Lee]

Last question! (sry...)

Is there any way to get r square value of the trendline?

Thanks!

[Star Strider]

That would be easiest using the fitnlm function. It will do the fit and produce many relevant statistics, including the R² value.