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Math Help - Regression by RMS method: Improving fit.

  1. #1
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    Feb 2010
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    Regression by RMS method: Improving fit.

    Hi all,

    I'm looking for some help with a regression problem.

    I have written a macro for Excel which fits a logarithmic function to a time series data set. The function I am using is:

    Y(x) = a*Ln(x + b) + c

    Where a, b and c are constants, x is the julian date (days after 1st Jan 1900).

    I input a guess for a, b and c the program than calculates the Sum of the Root Mean Squared residuals:

    SSR = √[∑(Y(x) Y(x))^2/n]

    Where Y(x) is the measured data at time x, and Y(x) is the fitted value. n is the number of data points.

    Excel then uses its Solver functionality to vary a, b and c to minimise SSR.

    The problem is when I run this macro the fits are very poor. By eye the data looks vaguely curved, possibly logarithmic. However, the fitted functions look linear and do not closely represent the data.

    I have speculated that the Solver is finding a local minimum of SSR, and not searching any further. In this case, could anyone suggest a way that I might improve my initial guesses of a, b and c to improve the chances of getting a closer fit?

    Otherwise could anyone suggest an alternative (improved?) regression method?

    I can show my code and/or a sample of the data if anyone is interested.

    Thanks in advance
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  2. #2
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    Feb 2010
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    Sorry, forgot to add that I may not be able to check this over the weekend. But will be back on Monday, hope this is ok.
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