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I want to regress v1 on o1:o7. I would like to do the same for each of v2:v5 with o1:o7. Is this possible?

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An excellent and very comprehensive answer has been given here to a related question. In summary, given the low number of samples, you will suffer from an inability to estimate parameters in a multiple regression. To estimate all the parameters, you will need k+2 samples to get parameter estimates with confidence intervals, or at least 9 samples for 7 predictors.

To your more general question of "can regression be of help", I would recommend you refine what exactly you mean. Do you mean help to predict v1 for new samples? Do you mean estimating parameters with a certain level of confidence? Etc. I think you will find better quality assistance with a more refined question.

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  • $\begingroup$ (+1) Especially for the 2nd paragraph - a precise statement of modelling goals needs to precede any discussion of e.g. regularization techniques. $\endgroup$ – Scortchi - Reinstate Monica May 5 '15 at 14:02

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