Regression analysis

Regression analysis is a field of statistics. It is a tool to show the relationship between the inputs and the outputs of a system. There are different ways to do this. Better curve fitting usually needs more complex calculations. 
"Data modeling" can be used without knowing about the underlying processes that have generated the data; in this case the model is an empirical model. Moreover, in modelling, knowledge of the probability distribution of the errors is not required. "Regression analysis" requires assumptions to be made regarding probability distribution of the errors. Statistical tests are made on the basis of these assumptions. In regression analysis the term "model" embraces both the function used to model the data and the assumptions concerning probability distributions.
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. 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.
The first type of regression analysis was linear regression. The method of least squares was first published by Legendre in 1805 and in 1809 by Gauß. Both used the method to predict the movement of planets around the sun. Gauss published an improved method in 1821.