įor Galton, regression had only this biological meaning, but his work was later extended by Udny Yule and Karl Pearson to a more general statistical context. The phenomenon was that the heights of descendants of tall ancestors tend to regress down towards a normal average (a phenomenon also known as regression toward the mean). The term "regression" was coined by Francis Galton in the 19th century to describe a biological phenomenon. Gauss published a further development of the theory of least squares in 1821, including a version of the Gauss–Markov theorem.
Legendre and Gauss both applied the method to the problem of determining, from astronomical observations, the orbits of bodies about the Sun (mostly comets, but also later the then newly discovered minor planets). The earliest form of regression was the method of least squares, which was published by Legendre in 1805, and by Gauss in 1809. The latter is especially important when researchers hope to estimate causal relationships using observational data. To use regressions for prediction or to infer causal relationships, respectively, a researcher must carefully justify why existing relationships have predictive power for a new context or why a relationship between two variables has a causal interpretation. Importantly, regressions by themselves only reveal relationships between a dependent variable and a collection of independent variables in a fixed dataset. Second, in some situations regression analysis can be used to infer causal relationships between the independent and dependent variables. First, regression analysis is widely used for prediction and forecasting, where its use has substantial overlap with the field of machine learning. Regression analysis is primarily used for two conceptually distinct purposes. Less common forms of regression use slightly different procedures to estimate alternative location parameters (e.g., quantile regression or Necessary Condition Analysis ) or estimate the conditional expectation across a broader collection of non-linear models (e.g., nonparametric regression). For specific mathematical reasons (see linear regression), this allows the researcher to estimate the conditional expectation (or population average value) of the dependent variable when the independent variables take on a given set of values. For example, the method of ordinary least squares computes the unique line (or hyperplane) that minimizes the sum of squared differences between the true data and that line (or hyperplane). The most common form of regression analysis is linear regression, in which one finds the line (or a more complex linear combination) that most closely fits the data according to a specific mathematical criterion. In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome' or 'response' variable, or a 'label' in machine learning parlance) and one or more independent variables (often called 'predictors', 'covariates', 'explanatory variables' or 'features').
Regression line for 50 random points in a Gaussian distribution around the line y=1.5x+2 (not shown)
#Do not regress meaning series
Set of statistical processes for estimating the relationships among variables Part of a series on
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