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I have a data set of 10 observations on 9 bivariate random variables (one is response & others are covariates). I want to fit a linear regression on the whole data set.

I want to know if there is any special technique to do so.

I can divide the data into two equal groups. Please suggest something for that situation also.

Thanks in advance for any kind of help/suggestion.

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    $\begingroup$ One thing to do would be to apply some form of regularization, such as shrinkage, such as by Lasso or possibly ridge regression. Another alternative - especially if the variables are in some sense related - might be to take the first few principal components and use those in the regression equation. $\endgroup$
    – Glen_b
    Commented Feb 9, 2014 at 6:24
  • $\begingroup$ (1) I might not know what I'm taking about. If you this is a clustered trial, 10 observations/clusters may be a fair number. Or 10 time series etc. (2) use domain knowledge to simplify model if possible (3) describe data rather than fit models/try to look for p-values. $\endgroup$
    – charles
    Commented Feb 9, 2014 at 17:16

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There are general solutions to the problem of more predictors than observations, including regularisation (such as LASSO), using a Bayesian prior (see Modelling with more variables than data points for more discussion of this), or random forests.

But the bigger problem here is that there are just 10 data points. It's not impossible but very unlikely that there's much you can learn from such a tiny dataset. There are circumstances in which such small datasets are informative e.g. you have a strong a priori hypothesis, or are measuring a calibration curve in a lab experiment. But these are unlikely to apply in your situation, which sounds more exploratory.

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