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( Regression analysis)
In statistics, regression analysis is a collective name for techniques for the modeling and analysis of numerical data consisting of values of a dependent variable (also called response variable or measurement) and of one or more independent variables (also known as explanatory variables or predictors). The dependent variable in the regression equation is modeled as a function of the independent variables, corresponding parameters ("constants"), and an error term. The error term is treated as a random variable. It represents unexplained variation in the dependent variable. The parameters are estimated so as to give a "best fit" of the data. Most commonly the best fit is evaluated by using the least squares method, but other criteria have also been used. Regression can be used for prediction (including forecasting of time-series data), inference, hypothesis testing, and modeling of causal relationships. These uses of regression rely heavily on the underlying assumptions being satisfied. Regression analysis has been criticized as being misused for these purposes in many cases where the appropriate assumptions cannot be verified to hold.[1][2] One factor contributing to the misuse of regression is that it can take considerably more skill to critique a model than to fit a model.[3] The earliest form of regression was the method of least squares, which was published by Legendre in 1805,[4] and by Gauss in 1809.[5] The term “least squares” is from Legendre’s term, moindres carrés. However, Gauss claimed that he had known the method since 1795. Legendre and Gauss both applied the method to the problem of determining, from astronomical observations, the orbits of bodies about the Sun. Euler had worked on the same problem (1748) without success.[citation needed] Gauss published a further development of the theory of least squares in 1821,[6] including a version of the Gauss–Markov theorem.
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