320_LectureNotes-Multiple Regression Analysis

320_LectureNotes-Multiple Regression Analysis - University...

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University of Oregon Rosie Mueller Department of Economics Fall 2016 Lecture: Multiple Regression Analysis (Chapter 3 in Dougherty, pages 151-184) EC 320: Econometrics Types of Data: Cross-Sectional Data: data on multiple unit of observation (i.e. people, states, etc.) at a single point in time (EAEF dataset in Homework 2 and 3) Time Series: data on a single unit of observation over time (P/E ratios dataset in Home- work 1) Panel: data on multiple units over time (ECON 421) In this class we will primarily focus on cross-sectional data. I. The Multiple Linear Regression Model Up to this point we have assumed there is just one independent variable. We estimate our population model: Y i = β 0 + β 1 X 1 i + u i and obtain our estimated model: Y i = b 0 + b 1 X i + e i Rarely does economic theory suggest a relationship between a dependent variable and and only a single independent variable. Ex: What else might affect earnings besides education level? Regression analysis with more than one independent variable is called multiple regression analysis . Suppose we have n observations on a dependent variable Y i , and k independent variables, denoted X 1 i , X 2 i , . . . X ki . The Multiple Linear Regression Model is: Y i = β 0 + β 1 X 1 i + β 2 X 2 i + . . . + β k X ki + u i β 0 , β 1 , β 2 , . . . β k are the parameters of the model β 0 is the intercept β 1 , β 2 , . . . β k are the slope parameters that tell us how Y i is influenced by X 1 i , X 2 i , . . . X ki u i is the disturbance term 1
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How do we interpret the parameters of the multiple linear regression model? β 1 measures the change in Y i that results from a one-unit change in X 1 i , holding constant all other variables in the regression. The holding constant part is important. Example : On the midterm we estimated how donut consumption affects weight. We estimated the model: Weight i = β 0 + β 1 Donuts i + u i Interpretation of β 1 : If a person eats one more donut per week, weight will increase by β 1 pounds, on average. In the estimated model, b 1 was about 9 and R 2 was about 0.67. However, there are certainly other independent variables that influence how much a person weighs, other than donut consumption. Some of these factors might be correlated with donut consumption. Do we really believe that weekly donut consumption is responsible for 67% of variation in body weight? The simple model is an over-simplification There is a lot of variation in weight that is left unexplained in the error term (What else should we include? We’re likely attributing too much variation in weight to donut consumption (Do men eat more donuts? Do people that exercise eat fewer donuts?) We could add a variable to indicate male or female, since this certainly explains part of the variation in bodyweight, since on average men weigh more than women. The variable Male is equal to 1 if the person is male, and 0 if the person is female. This is called a dummy variable .
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