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Math Help - Regression analysis Methodology - Is this the right approach?

  1. #1
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    Regression analysis Methodology - Is this the right approach?

    Hi I have a set of 10 data sets sampled over 10 years. For each year i estimate a statistic from the data.

    example

    x = 0,1,2,3,4,5,6,7,8,9,10
    y= 0.5,0.86,3,4,6,8.7,9.3,9.9,11 <-estimated statistic from my data

    For each estimated value I have a bootstrap distribution.

    I then fit several linear and nonlinear models to this data using least squares (e.g linear,polynomial,exponential,logistic).

    I am not thinking of using the chi square goodness of fit formula to find the best fit

    \chi^2 = 1/v \sum_{i=1}^{10}\frac{(O_i-E_i)^2}{\sigma_i^2} where v is the degrees of freedom and \sigma is the variance from my bootstraps.

    The model with \chi^2 closest to 1 is the model which best fits the data.

    -----------

    Does this methodology sound valid. I think the chi square test assumes my error distribution/bootstraps are normal. Can anyone recommend something better? or any criticisms
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  2. #2
    Grand Panjandrum
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    Re: Regression analysis Methodology - Is this the right approach?

    Quote Originally Posted by chogo View Post
    Hi I have a set of 10 data sets sampled over 10 years. For each year i estimate a statistic from the data.

    example

    x = 0,1,2,3,4,5,6,7,8,9,10
    y= 0.5,0.86,3,4,6,8.7,9.3,9.9,11 <-estimated statistic from my data

    For each estimated value I have a bootstrap distribution.

    I then fit several linear and nonlinear models to this data using least squares (e.g linear,polynomial,exponential,logistic).

    I am not thinking of using the chi square goodness of fit formula to find the best fit

    \chi^2 = 1/v \sum_{i=1}^{10}\frac{(O_i-E_i)^2}{\sigma_i^2} where v is the degrees of freedom and \sigma is the variance from my bootstraps.

    The model with \chi^2 closest to 1 is the model which best fits the data.

    -----------

    Does this methodology sound valid. I think the chi square test assumes my error distribution/bootstraps are normal. Can anyone recommend something better? or any criticisms
    I think we will need more context and/or detail about what you are trying to do here.

    CB
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  3. #3
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    Re: Regression analysis Methodology - Is this the right approach?

    Sorry Ill give some more information and my goal

    So as I described I have these 10 data sets sampled at times t_1,t_2,....,t_{10}. Specifically each data set is genetic data from influenza patients at time t_i.

    For each data set I calculate a statistic which summarizes the data. This statistic is just a simple counting method. Lets call the results from this statistic y_1,_y_2,....,y_{10}

    so now I am in a position to do some regression analysis on data [(t_1,y_1),....,(t_{10},y_{10})]

    Ok now because i wanted to know the distribution of my statistic I used a bootstrapping approach. Therefore for each time point I have a vector with the bootstrap distribution y^*_1,......,y_*_{10}.

    -----------------

    My Question/Goal - I want to fit a series of models to my data and then test which of these models best fits my data. i.e lets say an exponential model best fits my data.

    I though of using the chi square goodness of fit test for each model, but also i could use leave one out cross validation.

    Is this enough information? Thanks for your time, I hope this is slightly more clear
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