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Linear regression problem

  1. Feb 6, 2009 #1
    1. The problem statement, all variables and given/known data

    I've been given a set of data
    x 0 0.5 0.7 1.5 1.75
    y 0.5 0.72 0.51 1.5 1.63

    Given y=ax+b

    for this data points of linear model, I have to
    1. minimize the sum of the absolute values of deviations between experimental value of Y and value predicted by the linear relation
    2. minimiza the maximum value of deviation between all experimental values of Y and value predicted by linear relation

    The question is
    What are the optimal values of a and b for both cases and values of objective function.

    2. Relevant equations



    3. The attempt at a solution
    What I know is
    y=ax+b+e where e is the deviation but thats it. I don't even have the slightest idea for the next steps.
    I know seems simplebut I have very little background on linear regression.
    Help! T_T
     
  2. jcsd
  3. Feb 7, 2009 #2
    Hey, this is the first time I tried to help someone on this forum, so don't shoot me if I am wronge. If we are at the same level I guess you are supposed to use OLS Ordinary Least Square.

    b = [tex]\sum[/tex] (Xi-[tex]\bar{X}[/tex])(Yi-[tex]\bar{Y}[/tex])/
    [tex]\sum[/tex] (Xi-[tex]\bar{X}[/tex])2

    a = [tex]\bar{Y}[/tex] - b[tex]\bar{X}[/tex]

    where you sum from 1 to n.
    [tex]\bar{X}[/tex] means the average
     
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