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Math Help - Regression through the origin

  1. #1
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    Regression through the origin

    When I want to test if forcing the data to go through the origin is a good thing rather than just leaving it just the way it is, what value do i have to look at it?
    for instance, there is a data that i want to fit it so that it go through the origin. Then do i have to look at the p-value of intercept or F statistics value? or what do i have to look for if i wanna test 'passing through the origin' is a good thing.

    Thanks in advance
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  2. #2
    MHF Contributor matheagle's Avatar
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    All you need to do is leave out the intercept term in your model.

    Say,  Y=b_1x+b_2x^2 + \ldots +b_px^p + \epsilon.

    Now, if you're not interested in values near the origin, there's no reason to force your curve through that point.
    This will affect your other parameters.
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  3. #3
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    Quote Originally Posted by panda View Post
    When I want to test if forcing the data to go through the origin is a good thing rather than just leaving it just the way it is, what value do i have to look at it?
    for instance, there is a data that i want to fit it so that it go through the origin. Then do i have to look at the p-value of intercept or F statistics value? or what do i have to look for if i wanna test 'passing through the origin' is a good thing.
    There are two types of answers to your question:

    The "traditional statistics" answer would be to fit the data both ways and compare a statistic, such as you have mentioned.

    The "data mining" answer is to fit the data both ways, to a subset of the available observations (the "training data"). Then check the quality of each model by measuring, for instance, the mean absolute error on another. distinct subset of the available observations (the "validation data"). The model approach with the lower validation is selected and applied to the entire data set. You can read more about this technique in Section 14 of the Usenet comp.ai.neural-nets FAQ:

    What are the population, sample, training set, design set, validation set, and test set?


    -Will Dwinnell
    Data Mining in MATLAB
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