The successful vaccination implies the induction of effective specific immune responses. We intend to find biomarkers among various immune cell subpopulations, cytokines and antibodies which could be used to predict the levels of specific antibody- and cell-mediated responses after measles-mumps-rubella vaccination. We measured 59 baseline immune status parameters (frequencies of 42 immune cell subsets, levels of 13 cytokines, immunoglobulins) before vaccination and 13 response variables (specific IgA and IgG, antigen-induced IFN-γ production, CD107a expression on CD8+ T lymphocytes, and cellular proliferation levels by CFSE dilution) 6 weeks after vaccination for 19 individuals. Statistically significant Spearman correlations between some baseline parameters and response variables were found for each response variable (p<0.05). Due to the low number of observations relative to the number of baseline parameters and missing data for some observations, we utilized three feature selection strategies to select potential predictors of the post-vaccination responses among baseline variables: (a) screening of the variables based on the correlation analysis, (b) supervised screening based on the information of changes of baseline variables at day 7, (c) implicit feature selection is performed using regularization-based sparse regression. We identified optimal multivariate liner regression models for predicting the effectiveness of vaccination against measles-mumps-rubella using the baseline immune status parameters. It turned out that the sufficient number of predictor variables ranges from one to five depending on the response variable of interest.