Lecture+1+Review+SLR

Lecture+1+Review+SLR - Lecture1Review: Whatiseconometrics...

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1 Lecture 1 Review: The Simple Linear Regression What is econometrics? Econometrics is about using data to estimate and test economic relationships (existence, sign and magnitude) and make inference: What is the impact of unemployment insurance on unemployment rates/durations? What is the impact of education on wages? What is the impact of having overweight friends on your own weight? What is the impact of health insurance on health care utilization and health? In all these examples, there is a dependent variable , or Y that is the outcome of interest (unemployment, wages, probability of being overweight, health care utilization etc.), and an independent variable , or X of which the effect on the outcome we want to measure (unemployment insurance, education, having overweight friends, health insurance etc.) First we consider the simple linear regression (SLR) model. A simple linear regression model involves (1) one dependent variable Y ; (2) one independent variable or regressor X . It’s written as , YX u α β =+ + Assume it is the true population model . Some terminologies In the above simple linear regression model,
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2 and α β are regression coefficients (or parameters ) to be estimated; they are unknown constants . = intercept = slope We typically refer to Y as the Dependent Variable, Left-Hand Side Variable, Explained Variable, or Regressand. We typically refer to X as Independent Variable, Right-Hand Side Variable, Explanatory Variable, Regressor, Covariate. What is u here ? Example: Y =GPA, X =hours of study per week. GPA Study hours/week 3.5 25.0 2.0 10.0 2.2 12.0 3.5 15.0 2.5 20 Figure : A scatter plot of GPA and Study hours/week A coordinate system: good for displaying two variables on a single graph This graph is called a scatter plot . Note that the observations are not on a straight line ! This means that X and Y do not have an exact or deterministic linear relationship (Imagine they do,
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3 then once you have some data to estimate α and β , then you can predict the outcome Y with 100% accuracy for any given X ) For example, for any student, given his study time, you cannot precisely predict his GPA , even you have a large sample of data on both. So YX =+ won’t be right! Other variables that also affect GPA are left out, e.g. high‐school preparation, IQ, or pure luck on the day of test (one happens to guess half of the exam questions correctly). Alternatively, the dependent variable could have measurement errors, e.g., transcript records could be typed with errors. u is referred to as the error term or the unobservable, is an unobserved random variable that captures all the other variables that affect Y but are omitted from the above equation. When Y is mis‐measured, the measurement error also goes to u , since anything that is part of Y but is not captured by X goes to the error term u .
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Lecture+1+Review+SLR - Lecture1Review: Whatiseconometrics...

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