Obtaining Coefficients and Uncertainties for a Least-Squares Parabola

[diegojco]

I have tried to find some information of the expresions for a least-squares parabola coefficients (including their uncertaintities), then I have tried to do it for myself using the minimum condition for partial derivatives as same as with the least-squares line, but the expressions of coefs are so complex, and then I have no idea to obtain uncertaintities. In Matlab are a function to get the coefficients but not the uncertaintities, and I am upset, since I must get how to obtain uncertaintities, it's fundamental for a lab report on Maxwell's Disc.

Please Help Me!

 

[diegojco]

For the linear least-squares regression we can get:

y=ax+b

a=(Σxy-nx_meany_mean)/(Σ(x^2)-n(x_mean^2))

b=y_mean-ax_mean

and their uncertaintities:

Δa=sqrt((Σ((y-(ax)-b)^2))/(n-2))/sqrt(Σ(x^2)-n(x_mean^2))

Δb=sqrt((Σ((y-(ax)-b)^2))/(n-2))*sqrt((1/n)+((x_mean^2)/D))

where D=(Σ(x^2)-n(x_mean^2)). hence we have that the ecuation is:

y=(a±Δa)x+(b±Δb)

Well I'm triying to do the same for a parabolic least-squares.

 

[photon_mass]

for a parabolic least squares, you need to use logarithms.
/s

 

[photon_mass]

plot you graph on log paper. it should make a stright line.