The classification of observations is an important constituent of statistics and machine learning, either for analysis of data sets, or as a subgoal of a more complex problem. A novel machine learning technique, Support Vector Machines (SVM), has recently been receiving considerable attention in pattern recognition and regression function estimation problems. This paper uses standard logistic regression models for binary classification problems and compares them with SVM models with linear and non-linear kernel functions. An application with real data associated with giving birth to a low birth weight baby and patients with cancer of prostate are presented as an illustration. Based on the results of the numerical examples, it is determined that Support Vector Classification method produces remarkable results.