lec1 - I.Introduction ,whatarethe regression...

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I. Introduction: Simple Linear Regression

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As discussed last semester, what are the  basic differences  between correlation &  regression?  What vulnerabilities do correlation &  regression share in common?  What are the conceptual challenges  regarding causality?
Linear regression is a statistical method for  examining how an outcome variable  y   depends on one or more explanatory  variables  x .  E.g., what is the relationship of the per  capita earnings of households to their  numbers of members & their members’ ages,  years of higher education, race-ethnicity,  gender & employment statuses?

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What is the relationship of the fertility  rates of countries to their levels of GDP  per capita, urbanization, education, & so  on?  Linear regression is used extensively in  the social, policy, & other sciences.
Multiple regression—i.e. linear regression  with more than one explanatory variable —makes it possible to:   Combine many explanatory variables for  optimal understanding &/or prediction; &  Examine the unique contribution of each  explanatory variable, holding the levels of the  other variables constant.

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Hence, multiple regression enables us to  perform, in a setting of observational research,  a rough approximation to experimental  analysis.  Why, though, is  experimental  control better  than  statistical  control?  So, to some degree multiple regression  enables us to isolate the independent  relationships of particular explanatory variables  with an outcome variable.
So, concerning the relationship of the per  capita earnings of households to their  numbers of members & their members’ ages,  years of education, race-ethnicity, gender &  employment statuses:   What is the independent effect of years of  education on per capita household earnings,  holding the other variables constant?

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Regression is  linear   because it’s  based on a linear (i.e. straight line)  equation.  E.g., for every one-year increase in a  family member’s higher education (an  explanatory variable), household per  capita earnings increase by \$3127 on  average, holding the other variables  fixed.
But such a statistical finding raises  questions: e.g., is a year of college  equivalent to a year of graduate school  with regard to household earnings?  We’ll see that multiple regression can  accommodate nonlinear as well as  linear y/x relationships.

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This note was uploaded on 07/11/2011 for the course SYA 6306 taught by Professor Tardanico during the Spring '09 term at FIU.

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lec1 - I.Introduction ,whatarethe regression...

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