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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$\begingroup$ You can run regression on anything you want, but 3 rows is not going to give you a very accurate model. With so little data, it is even hard to reduce the number of variables. You might consider resampling the data. $\endgroup$– mandataCommented May 5, 2015 at 13:44
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$\begingroup$ possible duplicate of Maximum number of independent variables that can be entered into a multiple regression equation $\endgroup$– Sycorax ♦Commented May 5, 2015 at 13:47
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$\begingroup$ This is a rather extreme large $p$ small $n$ problem. See also here. $\endgroup$– Scortchi ♦Commented May 5, 2015 at 14:08
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$\begingroup$ Please read degrees of freedom $\endgroup$– kshaCommented Sep 4, 2017 at 13:17
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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 ♦Commented May 5, 2015 at 14:02