We present a general methodology for inferring the occurrence and magnitude of an event or phenomenon by exploring the rich amount of unstructured textual information on the social part of the web. Having geo-tagged user posts on the microblogging service of Twitter as our input data, we investigate two case studies. The first consists of a benchmark problem, where actual levels of rainfall in a given location and time are inferred from the content of tweets. The second one is a real-life task, where we infer regional Influenza-like Illness rates in the effort of detecting timely an emerging epidemic disease. Our analysis builds on a statistical learning framework, which performs sparse learning via the bootstrapped version of LASSO to select a consistent subset of textual features from a large amount of candidates. In both case studies, selected features indicate close semantic correlation with the target topics and inference, conducted by regression, has a significant performance, especially given the short length a?? approximately one year a?? of Twitter's data time series.