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edited May 28, 2010 at 16:47

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I am not sure what exactly you are looking for. But, looking at the data, a linear one dimensional model does not fit so well. To see this, try CCA (Canonical Correlation Analysis): the linear version computes two linear transforms of the input spaces, such that the transformed data are maximally correlated. I suspect from your data that the maximum correlation you will get is no more that 0.7-0.8. If you are looking to "explain the data", you need a generative model, perhaps a Gaussian Mixture for good results.

For the practical aspects of data analysis, you can try Handbook of Statistical Analysis and Data Mining Applications by Nisbet, Elder, Miner. If you look to understand the theory, The Elements of Statistical Learning by Hastie, Tibshirani and Friedman is the standard graduate text (though it might be too difficult, if you are not at ease with probability, measure theory and some functional analysis.) Good luck!

I am not sure what exactly you are looking for. But, looking at the data, a linear one dimensional model does not fit so well. To see this, try CCA (Canonical Correlation Analysis): the linear version computes two linear transforms of the input spaces, such that the transformed data are maximally correlated. I suspect from your data that the maximum correlation you will get is no more that 0.7-0.8. If you are looking to "explain the data", you need a generative model, perhaps a Gaussian Mixture for good results.

For the practical aspects of data analysis, you can try Handbook of Statistical Analysis and Data Mining Applications by Nisbet, Elder, Miner. If you look to understand the theory, The Elements of Statistical Learning by Hastie, Tibshirani and Friedman is the standard graduate text (though it might be too difficult, if you are not at ease with probability, measure theory and functional analysis.) Good luck!

I am not sure what exactly you are looking for. But, looking at the data, a linear one dimensional model does not fit so well. To see this, try CCA (Canonical Correlation Analysis): the linear version computes two linear transforms of the input spaces, such that the transformed data are maximally correlated. I suspect from your data that the maximum correlation you will get is no more that 0.7-0.8. If you are looking to "explain the data", you need a generative model, perhaps a Gaussian Mixture for good results.

For the practical aspects of data analysis, you can try Handbook of Statistical Analysis and Data Mining Applications by Nisbet, Elder, Miner. If you look to understand the theory, The Elements of Statistical Learning by Hastie, Tibshirani and Friedman is the standard graduate text (though it might be too difficult, if you are not at ease with probability, measure theory and some functional analysis.)

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created May 28, 2010 at 13:05

71
2
4

I am not sure what exactly you are looking for. But, looking at the data, a linear one dimensional model does not fit so well. To see this, try CCA (Canonical Correlation Analysis): the linear version computes two linear transforms of the input spaces, such that the transformed data are maximally correlated. I suspect from your data that the maximum correlation you will get is no more that 0.7-0.8. If you are looking to "explain the data", you need a generative model, perhaps a Gaussian Mixture for good results.

For the practical aspects of data analysis, you can try Handbook of Statistical Analysis and Data Mining Applications by Nisbet, Elder, Miner. If you look to understand the theory, The Elements of Statistical Learning by Hastie, Tibshirani and Friedman is the standard graduate text (though it might be too difficult, if you are not at ease with probability, measure theory and functional analysis.) Good luck!