322 Chapter 4

322 Chapter 4 - Introduction to Econometrics Chapter 4: The...

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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...
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322 Chapter 4 - Introduction to Econometrics Chapter 4: The...

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