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Unformatted text preview: The Linear Regression Model Estimating the Coe cients Fit The Least Squares Assumptions Sampling Distributions Introduction to Econometrics Chapter 4: The Linear Regression Model Geo rey Williams gwilliams@econ.rutgers.edu October 4, 2010 Geo rey Williams gwilliams@econ.rutgers.edu Introduction to Econometrics Chapter 4: The Linear Regres The Linear Regression Model Estimating the Coe cients Fit The Least Squares Assumptions Sampling Distributions 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 Linear Regression Model Estimating the Coe cients Fit The Least Squares Assumptions Sampling Distributions 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 The Linear Regression Model Estimating the Coe cients Fit The Least Squares Assumptions Sampling Distributions 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 The Linear Regression Model Estimating the Coe cients Fit The Least Squares Assumptions Sampling Distributions 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 The Linear Regression Model Estimating the Coe cients Fit The Least Squares Assumptions Sampling Distributions...
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This note was uploaded on 01/22/2012 for the course ECONOMICS 220:322 taught by Professor Otusbo during the Fall '10 term at Rutgers.
 Fall '10
 Otusbo
 Econometrics

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