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    Question Polynomial regression - Degree problem




    Hello,

    I would like to ask that how do I decide exactly what degree polynomial to use in my regression?

    I have attached the sample file.



    Thank you for the response!
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    Re: Polynomial regression - Degree problem

    Do you have any idea?

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    Re: Polynomial regression - Degree problem

    You need to provide much more detail. I have no idea what you are writing about, given I have not opened your attached file. What do you mean by poynomial regression (e.g, one of your IV or DV to a higher power)? You need to lay everything out so we have some understanding of your purpose or question.

    Thanks!
    Stop cowardice, ban guns!

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    Re: Polynomial regression - Degree problem

    Hello hlsmith,

    Thank you for your attention. Please bear with me, I'm beginner yet.
    In my sample file I would like to predict the future values (I have 11 months historical consumption data) based on polynomial regression but I do not have enough statistican knowledge to decide that how to determine what level of polynomial to use (3 or 4 or ??... I do not know). Do you know any kind of rule which is determine exactly this?

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    Re: Polynomial regression - Degree problem

    There are several types of polynomial regression in time series. And chosing which polynomial to use in any of them is complex (I spent weeks trying to figure out the advice and still largely failed).

    But the point hlsmith made is accurate. You need to provide more details on exactly you are trying to do.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Polynomial regression - Degree problem

    I'm stuck in therefore please, would you be so kind to tell me what kind of details would you need?

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    Re: Polynomial regression - Degree problem

    Well to start with what are you doing the regression for? What is the dependent variable and what is the independent variable?

    If you are trying to simply decide whether to fit a cubic or quadratic term than you can chose the terms that generates a model which has the best AIC. Or add a cubic and quadratic term and remove them if they are not signficant. But you should be basing on adding these terms on some theory not such empirical analysis.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Polynomial regression - Degree problem

    I would like to use the polynomial regression for the future material consumption prediction. I have some historical consumption data ( Range: B2:L3 --Month & Consumption--, these are the independent variables in my file) and my target is that to give a prediction for the next 11 months (Range: B6:L7 --Month & Consumption--, dependent variables).

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    Re: Polynomial regression - Degree problem

    So your question is what will consumption be by month for the next 12 months?

    I think the confusion is that there are many types of polynomial regression used for various purposes and other posters are not certain which you really are talking about. They vary so much that answering questions about them when you are not sure which a poster really is interested in is very difficult.

    To me it looks like what you are really trying to do is apply a non-linear model to regression (because you are assuming that the data in the future is a curve rather than a straight line I guess). A common way to do that is to add the quadratic term and see if it improves the adjusted R square value or other measure of model value. If it gets better than you keep the term if not you drop it. You then add a cubic term and do the same. Also you would check to see if the quadratic and cubic term is statistically significant.

    Whether that really is what you should be doing is a different question. Since you are modeling time series data essentially the regression model you are using may not be valid. Regression with autoregressive error might be better, exponenential smoothing is a lot simpler [Holt Winston]. You need about 50 data points at least to run what you want at the bare minimum. Issues like seasonality come into play here. In other words, if I understand what you are doing you are not applying an ideal method to do it.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Polynomial regression - Degree problem


    Thank you for your time and advice noetsi. Now I feel that I'm a bit closer to solve my problem.

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