Simple linear regression allows researchers to estimate the parameters—the intercept and slopes—of linear equations connecting two or more variables. Knowing that a dependent variable is functionally related to one or more independent or explanatory variables, and having an estimate of the parameters of that function, greatly improves the ability of a researcher to predict the values the dependent variable will take under many conditions. Being able to estimate the effect that one independent variable has on the value of the dependent variable in isolation from changes in other independent variables can be a powerful aid in decision making and policy design. Being able to test the existence of individual effects of a number of independent variables helps decision makers, researchers, and policy makers identify what variables are most important. Regression is a very powerful statistical tool in many ways.
The idea behind regression is simple, it is simply the equation of the line that "comes as close as possible to as many of the points as possible". The mathematics of regression are not so simple, however. Instead of trying to learn the math, most researchers use computers to find regression equations, so this chapter stressed reading computer printouts rather than the mathematics of regression.
Two other topics, which are related to each other and to regression, correlation and covariance, were also covered.
Something as powerful as linear regression must have limitations and problems. In following chapters those limitations, and ways to overcome some of them, will be discussed. There is a whole subject, econometrics, which deals with identifying and overcoming the limitations and problems of regression.
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