Differentiate partially wrt and equate each derivative to zero and solve the resulting equations.
I have been trying to find the values of the coefficients for the least squares parabola:
y = a + bx + cx^2
I have taken partial derivatives wrt a, b, c and now have three equations, but I don't know what to do next...any suggestions? Have you solved this before?
thank you very much!!
The equation that you should be differentiating is the one for
Differentiating wrt gives you
and on putting this equal to zero this can be rewritten as
The summations are taken over the data points and will therefore be numbers.
Differentiate to find the other two equations and then solve them simultaneously for and
BTW, do not double post. The response that you are getting from your other posting is an alternative method, they produce the same end result.
If you are working 'on paper', then a routine elimination is best.
Subtract multiples of the first equation from the second and third equations to eliminate say, from both of them, then take a multiple of one of the new equations from the other to eliminate
That allows you to calculate and you can back substitute to calculate and