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This project investigates a statistical method for analyzing the error on predictions made through the process of time-delay-embedding of chaotic time series. When viewed as a time-series, chaotic data appears to be unpredictable and random. A chaotic system actually has an orderly representation when viewed in its proper state space (the space consisting of the pertinent variables of the system). A very remarkable result from the study of chaotic dynamical systems shows that present in almost any single time series is information from all the variables of the state space. The technique of time-delay-embedding provides a method for making predictions on the evolution of this time series. In this method of prediction, one must choose a parameter k, the number of near neighbors in phase space to fit the model to. This project answers the question by describing an algorithm for determining the largest k such that the model adequately fits the data. A prediction is then made from this model along with confidence intervals which measure the reliability of the expected response. While this project involved many different data sets, the purpose was not to analyze these specific data sets, but to develop a general algorithm which could theoretically be used on any chaotic system.