No, classical regression techniques can not be used here. Since a number of variables are greater than a number of observations, it is a high dimension dataset and ordinary least squares cannot be considered for an estimate as standard deviation and variance will be infinite. We will have to use regression techniques such as Lasso, Ridge, etc. which will penalize coefficients and will reduce variance and standard deviation. Subset regression and/or stepwise regression can also be explored with a forward step approach.