CODEWITHSUNDEEP
curve-fitting
Ramanathan J
Ramanathan J

Reputation: 11

How to find least square fit for two combined functions

I have a curvefit problem

I have two functions

y = ax+b
y = ax^2+bx-2.3

I have one set of data each for the above functions

I need to find a and b using least square method combining both the functions

I was using fminsearch function to minimize the sum of squares of errors of these two functions.

I am unable to use this method in lsqcurvefit Kindly help me

Regards Ram

Upvotes: 1

Views: 730

Answers (2)

JJacquelin
JJacquelin

Reputation: 1705

y = ax+b

y = ax^2+bx-2.3

In order to not confuse y of the first equation with y of the second equation we use distinct notations :

u = ax+b

v = ax^2+bx+c

The method of linear regression combined for the two functions is shown on the joint page :

enter image description here

HINT : If you want to find by yourself the matrixial equation appearing above, follow the Gene's answer.

Upvotes: 1

Gene
Gene

Reputation: 46960

I think you'll need to worry less about which library routine to use and more about the math. Assuming you mean vertical offset least squares, then you'll want

D = sum_{i=1..m}(y_Li - a x_Li + b)^2 + sum_{i=j..n}(y_Pj - a x_Pj^2 - b x_Pj + 2.3)^2

where there are m points (x_Li, y_Li) on the line and n points (x_Pj, y_Pj) on the parabola. Now find partial derivatives of D with respect to a and b. Setting them to zero provides two linear equations in 2 unknowns, a and b. Solve this linear system.

Upvotes: 1

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