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Unformatted text preview: Inclass exerciseThe accompanying table shows the joint distribution between an individuals high school performance and his/her college performance. An individual is said to have performed poorly if his/her GPA is less than or equal to 2.5. Random variable X denotes whether the individual performed poorly in high school or not. Random variable Y shows whether the individual performed poorly in college or not. performed well in college poor college performance performed well in high school 0.591 0.148 poor high school performance 0.003 0.258 Y1YX1XQuestions1.Compute E(X) and interpret the result. 2.Calculate and interpret E(YX=0) 3. Conditional on the knowledge that the individual performed poorly in high school, what is the probability that the individual performed well in college? y= b+ b1x+ u The Simple Regression Model 4 OUTLINE 1.The Model: Definitions and Assumptions 2.Ordinary Least Squares (OLS) Estimates 3.Interpretation of estimates 4.An example 1. SIMPLE LINEAR REGRESSION (SLR) MODEL: DEFINITIONS & ASSUMPTIONSy and x are two variables, representing some population, and we are interested in determining the relationship between y and x. There are three issues with attempting to address this question: There is never an exact relationship between two variables, so we have to allow for other factors to affect y. We need to know the functional relationship between y and x. We need to be sure we are capturing a ceteris paribus relationship between y and x, if that is what is desired. 1. SLR MODEL: DEFINITIONS & ASSUMPTIONSWell resolve all three issues by writing the following equation: y= b+ b1 x + u This is known as the simple linear regression model. When related by the above equation, y and x have several different names that are used interchangeably, as shown in the table on the following slide. 1. SLR MODEL: DEFINITIONS & ASSUMPTIONS1. SLR MODEL: DEFINITIONS & ASSUMPTIONSy= b+ b1 x + u How does the above model help us address the three issues on the earlier slide? The variable u in the above model is called the error term, and it represents factors other than x that affect y. (The "u" stands for "unobserved.") The SLR model assumes a linear relationship between the variables yand x.If the other factors in u are held fixed, so that the change in u is zero (u=0), then: y = b1 x when u=0 b1is the slope parameterand captures the ceteris paribus (causal )effectof x on y. bis the intercept parameter. 9 Example: A simple wage equation  Population of all working individuals in the U.S.  Want to capture relationship between hourly wage and years for schooling wage= b0 +b1 educ + uwage is an individual hourly wage....
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This note was uploaded on 02/29/2012 for the course ECONOMICS 220:322 taught by Professor Otusbo during the Spring '10 term at Rutgers.
 Spring '10
 Otusbo
 Econometrics

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