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  Correlation and Regression Homework Help - K-12 Grade Level, College Level Mathematics

Introduction of Regression analysis

In statistics, Regression analysis is a statistical technique for estimating the relationships among variables. It includes various techniques for modeling and analyzing various variables, when the focus is on the relationship between a dependent variable and one or more independent variables. In particular, regression analysis helps one understand how the typical value of the dependent variable changes when any one of the independent variables is varied while the other independent variables are held fixed.

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Commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables -i.e. the average value of the dependent variable when the independent variables are fixed. Less generally the focus is on a quantile or other location parameter of the conditional distribution of the dependent variable given the independent variables. In all the cases the estimation target is a function of the independent variables called the regression function. In the regression analysis it is also of interest to characterize the variation of the dependent variable around the regression function, which can be described by probability distribution.

Correlation and dependence

Correlation refers to any of a broad class of statistical relationships involving dependence. In statistics, dependence refers to any statistical relationship between two random variables or two sets of data.

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Well-known examples of dependent phenomena include the correlation between the physical statures of parents and their offsprings, and the correlation between the demand for a product and its price. Correlation is useful because they can indicate a predictive relationship that can be exploited in practice. For illustration, an electrical utility may produce less power on a mild day based on the correlation between electricity demand and weather. In this illustration there is a causal relationship because extreme weather causes people to use more electricity for heating or cooling; though, statistical dependence is not sufficient to demonstrate the presence of such a causal relationship (i.e., Correlation does not imply causation).

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