Using regularization with logistic regression I have a data set of 3000 observations with 9 variables, and I'm trying to predict whether water are safe for drinking.
Regular multivariate logistic regression isn't that good at forecasting, and also none of the coefficients is significant, even if I run univariate logistic regression.
This is why I thought of regularization, but I wasn't able to found an explanation of this and when it is appropriate to use.
Also, if it exists, if be happy for a reference to R functions.

Regularisation aims at reducing the effects of design matrix being overdetermined or underdetermined, recall solving $Ax=b$, $A \in \mathbb{R}^{m \times p}$. Regularisation is appropriate to use if $p>>m$ (underdetermined) or $p<<m$ (overdetermined). Here the case is $m>>p$, overdetermined (m=3000, p=9 in this case).
Using LASSO or elastic net regularisation are recommended instead of plain logistic regression. Without regularisation, solution may not be correct. glmnet's introduction will give a good idea how to use LASSO and elastic-net regularisations.
See also rank deficiency.
