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finding a coefficient from an equation

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Ana Monea
Ana Monea on 18 May 2020
Commented: Ana Monea on 18 May 2020
Hello, i m a beginner on matlab and i would need some help. I have 2 vectors x and z with 10 values each and the equation z=c*sqrt(x). I have to find the value of c. Help please.
  3 Comments
Walter Roberson
Walter Roberson on 18 May 2020
In that case either use / or \ operators with appropriate arguments. They will do a least-squared fitting to find the best value for c.

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Answers (1)

Ang Feng
Ang Feng on 18 May 2020
(1)If your vectors x and x follows exactly z=c*sqrt(x), then the constant c can be calculated, as mentioned by Adam Danz,
c = sqrt(x)./z
You have a vector c which has 10 identical value which is what you are looking for.
(2) In the case x, and z just follow then trend of z=c*sqrt(x), you are actually asking for a constant c that minimize some function of the error vector. Normally, we minimize norm of the square of the error . This is a least square problem. You can actually use the curve fitting tool box to fit the function.
sqrtX = sqrt(x);
f = fit(sqrtX,z,'poly1');
c = f.p1;
Here is my little example.
x = (1:10)';sqrtX = sqrt(x);
z = 2*sqrtX+0.05*randn(10,1);% add some noise
f = fit(sqrtX,z,'poly1');
c = f.p1
ans =
1.9725
The parameter c = 2 was calculated to be 1.9725.

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