Statistical models use mathematical equations to encode information extracted from the data. Linear regression models attempt to find a straight line or surface through the range of input fields that minimizes the discrepancies between predicted and observed output values.
Logistic regression models are somewhat more complicated but use a similar strategy to generate equations for predicting probabilities associated with each possible value of a symbolic output field.
Statistical models have been around for some time and are relatively well understood mathematically. They represent basic models that assume fairly simple kinds of relationships in the data. In some cases, they can give you adequate models very quickly. Even for problems in which more flexible machine-learning techniques (such as neural networks) can ultimately give better results, you can use statistical models as baseline predictive models to judge the performance of advanced techniques.
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