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Thread: multiple regression equations

  1. #1
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    multiple regression equations

    hello,
    can anyone give a suggestion or reference regarding how a system of multiple regression equations are solved?
    rajesh

  2. #2
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    You should be able to use SPSS. There are some other techniques like Neural networks and Evolutionary Algorithms to solve/predict Multi variable problems.

  3. #3
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    Here I have tried to have a simple look into solving multiple regression.
    Any misunderstandings, please notify.

    Assumptions:
    1. Two independent variables SST (S) and Wind (W) and dependent variable
    Precipitation (P). Suppose we can say P=aS + bW
    'a' represents an estimate of the change in P corresponding to a one-unit
    change in S when all other independent variables(here W) are held constant.
    Similarily, 'b'.

    2. We have some values of P, S and W. With that, we want to make a
    predictor model which gives the relationship. i.e. the constants a and b.

    The "best" combination of a and b values is the combination that minimizes
    the sum of squares of the difference between the dependent variable and
    the dependent variable predicted by the model.

    This sum square of differences:
    SSD= ∑(Pi - Ppi)2
    SSD= ∑(Pi - (a * Si + b * Wi)) 2

    where Pi, Si and Wi [i=1 to N], known
    Ppi = Pp[i=1 to N], unknown

    note that the sequences Pi, Si, and Wi are deviations from mean.
    i.e. Pi=Pi(original)-P(average)


    A partial derivative of the above equation (w.r.to a and b) set to zero
    will give two equations for a and b in which a and b gives the least sum of
    differences.

    δSSD/δa = 0
    δSSD/δb = 0

    This will be:

    a = [∑(SiPi) * ∑(Wi2) - ∑(SiWi) * ∑(WiPi)] / [∑(Si2) * ∑(Wi2 ) - ∑(SiWi) * ∑(SiWi)]

    b = [∑(SiPi) * ∑(SiWi) - ∑(Si2) * ∑(WiPi)] / [∑(SiWi) * ∑(SiWi) - ∑(Si2) * ∑(Wi2 )]

    thus you will get a perdictor model:
    P = aS + bW in which you can put S, W and get P.

    'a' and 'b' can be found out by giving Si,Wi and Pi as input to a software
    which does regression. You will also get the error-intercept values as well.
    Maybe fortran functions can be used for it. In MatLab, there are a lot
    of regression functions starting from regress(). Just type in >> lookfor regress.
    Also a toolbox in MatLab, glmlab is referred for analysis including multiple regressions.
    http://www.sci.usq.edu.au/staff/dunn/glmlab/glmlab.html

    I think someone else can add on to this and give a developed version of this.

  4. #4
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    hello roxy,
    thanks for assistance. i will look into that.
    rajesh

  5. #5
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    hello all,
    i installed glmlab in matlab, but when typing glmlab i get this error message.

    >> glmlab
    ??? Undefined function or variable 'dllist'.

    Error in ==> D:\programs\toolbox\matlab\glmlab\glmlab.m
    On line 85 ==> L1=dllist(which('llist'),'l'); %load link functions

    why is it so? is anybody familiar?

    rajesh

  6. #6
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    hi, I just downloaded it and checked.
    Maybe you missed to Set Path of glmlab with subfolders.

    File-> Set Path -> Add with subfolders-> Select the folder where
    you unzipped glmlab. Save and Close.

    Then, I havent used glmlab though I saw many references to it.
    If it is useful, do tell. Try the built-in functions with matlab too.

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