This preview shows pages 1–8. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Introduction to Econometrics Chapter 4: The Linear Regression Model Geo rey Williams gwilliams@econ.rutgers.edu February 25, 2010 Geo rey Williams gwilliams@econ.rutgers.edu Introduction to Econometrics Chapter 4: The Linear Regres An Empirical Question Say we want to gure out the ideal class size for a school. We need to understand how an output (let's say test scores) vary with class size What's a simple way of denoting this relationship? Perhaps we can note how change in class size a ects change in test score Something like ClassSize ! TestScore An easier way is the ratio: ClassSize = TestScore ClassSize Geo rey Williams gwilliams@econ.rutgers.edu Introduction to Econometrics Chapter 4: The Linear Regres The value of ClassSize You can see how ClassSize could be a pretty valuable thing to know! With it, you can (in theory) predict the change in test score for any change class size TestScore = ClassSize ClassSize Geo rey Williams gwilliams@econ.rutgers.edu Introduction to Econometrics Chapter 4: The Linear Regres We add two components... Of course, it's even more valuable if we know the speci c test score to expect for any class size We'd need to add a constant, and rm up the equation TestScore = + ClassSize ClassSize In real life, of course, there are other factors that have an impact on a class's achievement levels (resources, aptitude, parental involvement, etc etc). We add those in: TestScore = + ClassSize ClassSize + Other Factors And voila, we have a simple linear regression model. Geo rey Williams gwilliams@econ.rutgers.edu Introduction to Econometrics Chapter 4: The Linear Regres Let's make it more formal... Let's say for a sample of n school districts, for each school district i we measure average class size X i and average test score Y i , and nd the relationship: Y i = + 1 X i + u i Let's give the terminology: Y i is the dependent variable or left hand side variable is the constant or intercept term 1 is the slope X i is the independent variable or right hand side variable u i is the error term Geo rey Williams gwilliams@econ.rutgers.edu Introduction to Econometrics Chapter 4: The Linear Regres Geo rey Williams gwilliams@econ.rutgers.edu Introduction to Econometrics Chapter 4: The Linear Regres Geo rey Williams gwilliams@econ.rutgers.edu Introduction to Econometrics Chapter 4: The Linear Regres Ordinary Least Squares...
View Full
Document
 Fall '10
 MacroWilliams,MicroYoshi

Click to edit the document details