2.

In statistics AU111: The URL http://en.wikipedia.org/wiki/Statistics has been redirected to https://en.wikipedia.org/wiki/Statistics. Please verify the URL. ,

**regression analysis** is a statistical process for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable AU112: The URL http://en.wikipedia.org/wiki/Dependent_variable has been redirected to https://en.wikipedia.org/wiki/Dependent_variable. Please verify the URL. and one or more independent variables AU113: The URL http://en.wikipedia.org/wiki/Independent_variable has been redirected to https://en.wikipedia.org/wiki/Independent_variable. Please verify the URL. . More specifically,

**regression analysis** helps one understand how the typical value of the dependent variable (or 'criterion variable') changes when any one of the independent variables is varied, while the other independent variables are held fixed. Most commonly,

**regression analysis** estimates the conditional expectation AU114: The URL http://en.wikipedia.org/wiki/Conditional_expectation has been redirected to https://en.wikipedia.org/wiki/Conditional_expectation. Please verify the URL. of the dependent variable given the independent variables – that is, the average value AU115: The URL http://en.wikipedia.org/wiki/Average_value has been redirected to https://en.wikipedia.org/wiki/Average_value. Please verify the URL. of the dependent variable when the independent variables are fixed. Less commonly, the focus is on a quantile AU116: The URL http://en.wikipedia.org/wiki/Quantile has been redirected to https://en.wikipedia.org/wiki/Quantile. Please verify the URL. , or other location parameter AU117: The URL http://en.wikipedia.org/wiki/Location_parameter has been redirected to https://en.wikipedia.org/wiki/Location_parameter. Please verify the URL. of the conditional distribution of the dependent variable given the independent variables. In all cases, the estimation target is a function AU118: The URL http://en.wikipedia.org/wiki/Function_(mathematics) has been redirected to https://en.wikipedia.org/wiki/Function_(mathematics). Please verify the URL. of the independent variables called the

**regression** function. In

**regression analysis**, it is also of interest to characterize the variation of the dependent variable around the

**regression** function which can be described by a probability distribution AU119: The URL http://en.wikipedia.org/wiki/Probability_distribution has been redirected to https://en.wikipedia.org/wiki/Probability_distribution. Please verify the URL. .

**Regression analysis** is widely used for prediction AU120: The URL http://en.wikipedia.org/wiki/Prediction has been redirected to https://en.wikipedia.org/wiki/Prediction. Please verify the URL. and forecasting AU121: The URL http://en.wikipedia.org/wiki/Forecasting has been redirected to https://en.wikipedia.org/wiki/Forecasting. Please verify the URL. , where its use has substantial overlap with the field of machine learning AU122: The URL http://en.wikipedia.org/wiki/Machine_learning has been redirected to https://en.wikipedia.org/wiki/Machine_learning. Please verify the URL. .

**Regression analysis** is also used to understand which among the independent variables are related to the dependent variable, and to explore the forms of these relationships. In restricted circumstances,

**regression analysis** can be used to infer causal relationships AU123: The URL http://en.wikipedia.org/wiki/Causality has been redirected to https://en.wikipedia.org/wiki/Causality. Please verify the URL. between the independent and dependent variables. However this can lead to illusions or false relationships, so caution is advisable; for example, correlation does not imply causation AU124: The URL http://en.wikipedia.org/wiki/Correlation_does_not_imply_causation has been redirected to https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation. Please verify the URL. . Many techniques for carrying out

**regression analysis** have been developed. Familiar methods such as linear

**regression** AU125: The URL http://en.wikipedia.org/wiki/Linear_

**regression** has been redirected to https://en.wikipedia.org/wiki/Linear_

**regression**. Please verify the URL. and ordinary least squares AU126: The URL http://en.wikipedia.org/wiki/Ordinary_least_squares has been redirected to https://en.wikipedia.org/wiki/Ordinary_least_squares. Please verify the URL.

**regression** are parametric AU127: The URL http://en.wikipedia.org/wiki/Parametric_statistics has been redirected to https://en.wikipedia.org/wiki/Parametric_statistics. Please verify the URL. , in that the

**regression** function is defined in terms of a finite number of unknown parameters AU128: The URL http://en.wikipedia.org/wiki/Parameter has been redirected to https://en.wikipedia.org/wiki/Parameter. Please verify the URL. that are estimated from the data AU129: The URL http://en.wikipedia.org/wiki/Data has been redirected to https://en.wikipedia.org/wiki/Data. Please verify the URL. . Nonparametric

**regression** AU130: The URL http://en.wikipedia.org/wiki/Nonparametric_

**regression** has been redirected to https://en.wikipedia.org/wiki/Nonparametric_

**regression**. Please verify the URL. refers to techniques that allow the

**regression** function to lie in a specified set of functions AU131: The URL http://en.wikipedia.org/wiki/Function_(mathematics) has been redirected to https://en.wikipedia.org/wiki/Function_(mathematics). Please verify the URL. , which may be infinite-dimensional AU132: The URL http://en.wikipedia.org/wiki/Dimension has been redirected to https://en.wikipedia.org/wiki/Dimension. Please verify the URL. . The performance of

**regression analysis** methods in practice depends on the form of the data generating process AU133: The URL http://en.wikipedia.org/wiki/Data_generating_process has been redirected to https://en.wikipedia.org/wiki/Data_generating_process. Please verify the URL. , and how it relates to the

**regression** approach being used. Since the true form of the data-generating process is generally not known,

**regression analysis** often depends to some extent on making assumptions about this process. These assumptions are sometimes testable if a sufficient quantity of data is available.

**Regression** models for prediction are often useful even when the assumptions are moderately violated, although they may not perform optimally. However, in many applications, especially with small effects AU134: The URL http://en.wikipedia.org/wiki/Effect_size has been redirected to https://en.wikipedia.org/wiki/Effect_size. Please verify the URL. or questions of causality based on observational data AU135: The URL http://en.wikipedia.org/wiki/Observational_study has been redirected to https://en.wikipedia.org/wiki/Observational_study. Please verify the URL. ,

**regression** methods can give misleading results.

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