Cough is the most common symptom of several respiratory diseases. It is a defense mechanism of the body to clear the respiratory tract from foreign materials inhaled accidentally or produced internally by infections. The identification of wet and dry cough is an important clinical finding, aiding in the differential diagnosis especially in children. Wet coughs are more likely to be associated with lower respiratory track bacterial infections. At present during a typical consultation session, the wet/dry decision is based on the subjective judgment of a physician. It is not available for the non-trained person, long term monitoring or in the assessment of treatment efficacy. In this paper we address these issues and develop an automated technology to classify cough into 'wet' and 'dry' categories. We propose novel features and a Logistic regression model (LRM) for the classification of coughs into wet/dry classes. The performance of the method was evaluated on a clinical database of pediatric coughs (C = 536) recorded using a bed-side non-contact microphone from N = 78 patients. Results of the automatic classification were compared against two expert human scorers. The sensitivity and specificity of the LRM in picking wet coughs were between 87 and 88% with 95% confidence interval on training/validation dataset (310 cough events from 60 patients) and 84 and 76% respectively on prospective dataset (117 cough events from 18 patients). The kappa agreement with two expert human scorers on prospective dataset was 0.51. These results indicate the potential of the method as a useful clinical tool for cough monitoring, especially at home settings.