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Least-squares parabola

  1. Oct 22, 2004 #1
    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!!
     
  2. jcsd
  3. Oct 23, 2004 #2
    For the linear least-squares regression we can get:

    y=ax+b

    a=(Σxy-nxmeanymean)/(Σ(x^2)-n(xmean^2))

    b=ymean-axmean

    and their uncertaintities:

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

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

    where D=(Σ(x^2)-n(xmean^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.
     
  4. Oct 23, 2004 #3
    for a parabolic least squares, you need to use logarithms.
    /s
     
  5. Oct 23, 2004 #4
    plot you graph on log paper. it should make a stright line.
     
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