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Lecture Undergraduate econometrics, 2nd edition - Chapter 6: The simple linear regression model

Chapter 6 - The simple linear regression model: reporting the results and choosing the functional form. In this chapter we will consider: How to measure the variation in yt explained by the model, how to report the results of a regression analysis, some alternative functional forms that may be used to represent possible relationships between yt and xt. | Chapter 6 The Simple Linear Regression Model Reporting the Results and Choosing the Functional Form To complete the analysis of the simple linear regression model in this chapter we will consider How to measure the variation in yt explained by the model How to report the results of a regression analysis Some alternative functional forms that may be used to represent possible relationships between yt and xt Slide 6.1 Undergraduate Econometrics 2nd Edition-Chapter 6 6.1 The Coefficient of Determination Two major reasons for analyzing the model yt P1 p2 t et 6.1.1 are 1. to explain how the dependent variable yt changes as the independent variable xt changes and 2. to predict y0 given an x0. Closely allied with the prediction problem is the desire to use xt to explain as much of the variation in the dependent variable yt as possible. Slide 6.2 Undergraduate Econometrics 2nd Edition-Chapter 6 In Equation 6.1.1 we introduce the explanatory variable xt in hope that its variation will explain the variation in yt. To develop a measure of the variation in yt that is explained by the model we begin by separating yt into its explainable and unexplainable components. We have assumed that yt E yt et 6.1.2 where E yt p1 p2xt is the explainable systematic component of yt and et is the random unsystematic unexplainable noise component of yt. We can estimate the unknown parameters p1 and p2 and decompose the value ofyt into yt y e 6.1.3 Slide 6.3 Undergraduate Econometrics 2nd Edition-Chapter