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Math Help - Multi Input Single Output Problem

  1. #1
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    Multi Input Single Output Problem

    I am trying to create some equations for a single output and multiple inputs. I am recording many inputs from a website and taking a single output from a solar power station near my house. But I have never tried making equations for this before. I have done single input single output in the form of curve fitting or making a spline but never a multiple input single output as I am attempting now. Does anyone have any advice on how to attempt to do something like this.

    Thanks
    Chris
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  2. #2
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    Quote Originally Posted by solidsnake5698 View Post
    Does anyone have any advice on how to attempt to do something like this.
    I am not really sure what you are asking.

    In complex analysis, it is useful to consider something called multi-valued functions.

    Example: The complex function f(z) = \sqrt[n]{z} gives us n values for non-zero z. So if n=2 and z=1 then f(z) = \{+1,-1\}.

    The above illustrates the situation when you have 1 input you get many outputs.

    Another example, with infinite outputs, is the logarithm function (complex). Defined as \mbox{Log}(z) = \{\log z + 2\pi n i \} for z\not = 0.

    Is this related to your question?
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  3. #3
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    Sorry, I guess I was a little to vague. I am analyzing solar panels this summer for some research, and I need to come up with some equations to predict how much solar energy I am getting. Therefore I am taking data from accuweather.com and hoping to be able to relate that data to the amount of power given from my solar system. I would consider the information from accuweather my multiple inputs and the amount of power my single output. So, I was wondering if there is anyway to come up with equations like this.

    Of course, you are asking yourself why don't you look for previously published equations. Well I did and had good luck finding them, but I am ahead of schedule on my project and my professor wants me to look into this.

    Does that make more sense if not I can try again.

    Chris
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  4. #4
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    Quote Originally Posted by solidsnake5698 View Post
    Sorry, I guess I was a little to vague. I am analyzing solar panels this summer for some research, and I need to come up with some equations to predict how much solar energy I am getting. Therefore I am taking data from accuweather.com and hoping to be able to relate that data to the amount of power given from my solar system. I would consider the information from accuweather my multiple inputs and the amount of power my single output. So, I was wondering if there is anyway to come up with equations like this.

    Of course, you are asking yourself why don't you look for previously published equations. Well I did and had good luck finding them, but I am ahead of schedule on my project and my professor wants me to look into this.

    Does that make more sense if not I can try again.

    Chris
    This sounds like a linear regression problem. For example, suppose you have data on one output Y and 3 inputs R, S, T like this.

    Code:
     Y    R    S    T
    25   80   52   26
    29   89   53   23
    31   78   46   15
    etc
    Linear regression allows you to find the best equation for predicting Y of the form

    Y = a + bR + cS + dT

    where a, b, c and d are constants fitted using your data. Is that what you are looking for?
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  5. #5
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    Is that what you are looking for?
    Why yes, JakeD, it sounds like it. Is there any particular website that could give me help on this topic or could you just share the information. I do have Maple 10 if you are familiar enough with that program. If you could point me in the right direction I would be thrilled.

    Thanks
    Chris
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  6. #6
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    Quote Originally Posted by JakeD View Post
    This sounds like a linear regression problem. For example, suppose you have data on one output Y and 3 inputs R, S, T like this.

    Code:
     Y    R    S    T
    25   80   52   26
    29   89   53   23
    31   78   46   15
    etc
    Linear regression allows you to find the best equation for predicting Y of the form

    Y = a + bR + cS + dT

    where a, b, c and d are constants fitted using your data. Is that what you are looking for?
    Quote Originally Posted by solidsnake5698 View Post
    Why yes, JakeD, it sounds like it. Is there any particular website that could give me help on this topic or could you just share the information. I do have Maple 10 if you are familiar enough with that program. If you could point me in the right direction I would be thrilled.

    Thanks
    Chris
    I provided a link to the the Wikipedia page on linear regression. Did you see that and try it?
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  7. #7
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    Sorry, no I didn't I am off to learn YEAH!!!

    Thanks again
    Chris
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  8. #8
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    Quote Originally Posted by JakeD View Post
    This sounds like a linear regression problem. For example, suppose you have data on one output Y and 3 inputs R, S, T like this.

    Code:
     Y    R    S    T
    25   80   52   26
    29   89   53   23
    31   78   46   15
    etc
    Linear regression allows you to find the best equation for predicting Y of the form

    Y = a + bR + cS + dT

    where a, b, c and d are constants fitted using your data. Is that what you are looking for?
    This assumes that a linear model of the relationship between inputes and
    output is adequate. One method I have seen used for what is essentialy non-
    linear regression with unknown functional realationship between inputes and
    the output is to use evolutionary algorithms to determine the relationship,
    where the genes represent the presence of abscence of particular types of
    non-linearity.

    RonL
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