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Math Help - Modelling From Data

  1. #1
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    Modelling From Data

    Howdy All,


    In class we are modelling from data, including linear, exponential, power, logarithmic and quadratic models.


    Normally, to find the correct model, I would use the R2 value, however, our teacher has now informed us that this is not a valid argument.

    What others arguments could I put forward to state that the model of best fit is each of these forms (linear, exponential etc.)?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by PrinceOfParadox View Post
    Howdy All,


    In class we are modelling from data, including linear, exponential, power, logarithmic and quadratic models.


    Normally, to find the correct model, I would use the R2 value, however, our teacher has now informed us that this is not a valid argument.

    What others arguments could I put forward to state that the model of best fit is each of these forms (linear, exponential etc.)?
    There is no one way of doing this, but a number of techniques can be of
    some use.

    1. Plot the residuals against the independent variable. They should be
    randomly scattered above and below 0 for a good model. The should not
    approximately follow some smooth curve.

    2. For a homoscadastic process the scatter of the points on the residual
    plot should not increase of decrease with the independent variable.

    3. The histogram of residuals should be approximately normal.

    RonL
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  3. #3
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    How do I plot said residuals against the independent variable?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by PrinceOfParadox View Post
    How do I plot said residuals against the independent variable?
    We have data: x1, x2, x3, ..., xN ; y1, y2, ... , yN, where xi is the
    independent variable (time or something like that) and yi the corresponding
    observed value of the dependent variable (population, concentration ...)

    We have a model Y(x) which allows us to predict from the model what we
    would expect the values of the y's to be at the corresponding x's.

    The residuals are: Ri = (yi -Y(xi)), i=1, .., N
    they are the differences between the observations and the model
    predictions, in a sense the unmodelled part of the variation in the y's.

    The residual plot is a plot of the x's against the corresponding R's.

    For a good model the residulal plot should be a more or less random
    scatter about the line R=0.

    RonL
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