The general purpose of regression analysis is to study the relationship between one or more dependent variable(s) and one or more independent variable(s). The most basic form of a regression model is where there is one independent variable and one dependent variable. For instance, a model relating the log of wage of married women to their experience in the work force is a simple linear regression model given by log(wage) = β0 + β1exper + ε, where β0 and β1 are unknown coefficients ande is random error. One objective here is to determine what effect (if any) the variable exper has on wage. In practice, most studies involve cases where there is more than one independent variable. As an example, we can extend the simple model relating log(wage) to exper by including the square of the experience (exper2) in the work force, along with years of education (educ). The objective here may be to determine what effect (if any) the explanatory variables (exper, exper2, educ) have on the response variable log(wage). The extended model can be written as


where β0, β1, β2, and β3 are the unknown coefficients that need to be estimated, and ε is random error.

An extension of the multiple regression model (with one dependent variable) is the multivariate regression model where there is more than one dependent variable. For instance, the well-known ...

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