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Unformatted text preview: Ordinary least squares (OLS) Interpretation and R 2 Econ 281  Chapter 1 Review  Simple Regression Analysis Richard Walker Northwestern University January 11, 2010 Econ 281  Chapter 1 Richard Walker Ordinary least squares (OLS) Interpretation and R 2 1 Ordinary least squares (OLS) Simple linear model Least squares regression 2 Interpretation and R 2 Interpretation of results Goodness of fit: R 2 Econ 281  Chapter 1 Richard Walker Ordinary least squares (OLS) Interpretation and R 2 1 Ordinary least squares (OLS) Simple linear model Least squares regression 2 Interpretation and R 2 Interpretation of results Goodness of fit: R 2 Econ 281  Chapter 1 Richard Walker Ordinary least squares (OLS) Interpretation and R 2 Simple linear model 1 Ordinary least squares (OLS) Simple linear model Least squares regression 2 Interpretation and R 2 Interpretation of results Goodness of fit: R 2 Econ 281  Chapter 1 Richard Walker Ordinary least squares (OLS) Interpretation and R 2 Simple linear model We want to start looking for relationships between economic variables We’re going to start with the most straightforward possible such relationship one dependent variable Y that we are trying to explain one explanatory variable X that might help us explain Y any relationship between X and Y is assumed a priori to be linear This is known as ‘simple linear regression’ ‘simple’ because there’s only one explanatory variable X Econ 281  Chapter 1 Richard Walker Ordinary least squares (OLS) Interpretation and R 2 Simple linear model We will assume that the following is the ‘true’ process by which the dependent variable Y is generated: Y i = β 1 + β 2 X i + u i (1.1) β 1 and β 2 are parameters that we would like to estimate u is a disturbance term The i subscript refers to the particular observation of the variables for example, if we are examining the relationship between height and wages across people, then the i would refer to the people we only actually ‘observe’ the Y i and X i , not the u i Econ 281  Chapter 1 Richard Walker Ordinary least squares (OLS) Interpretation and R 2 Simple linear model Y X β 1 Y = β 1 + β 2 X u i The true, datagenerating model Econ 281  Chapter 1 Richard Walker Ordinary least squares (OLS) Interpretation and R 2 Simple linear model Why is there a disturbance term? Why isn’t the relationship between Y and X ‘exact’? Omitted variables : something else also helps explain Y Aggregation : often the relationship is an aggregate one e.g. addingup lots of little consumption functions ⇒ aggregate consumption function unlikely to be exact Model misspecification : Y might depend on yesterday’s X , or the expectation of tomorrow’s X , rather than X itself relationship between Y and X will be close, but not exact Functional misspecification : maybe the relationship is nonlinear?...
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 Spring '10
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 Regression Analysis, Ordinary least squares, Richard Walker

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