lecture%206_s

# lecture%206_s - In-class exercise•There are 5 nobel...

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Unformatted text preview: In-class exercise•There are 5 nobel prizes awarded each year: physics, chemistry, peace, medicine and literature. In 1968, the Bank of Sweden added a sixth nobel prize for economics. X: is a random variable that denotes whether the person won the Economics or non-Economics nobel prize. Y: denotes whether the recipient is a U.S. or non-U.S. citizen. The table indicates the joint pdf between X and Y. X/YY=0 (U.S. citizen)Y=1( non-U.S. citizen)X=0 (Economics)0.1180.049X=1 (non-Economics)0.3450.488Questions1.Compute E(Y) and interpret the result. 2.Calculate and interpret E(Y|X=1) 3.A randomly selected nobel prize winner reports that he is a non-U.S. citizen. What is the probability that he has won the Economics nobel prize? 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 & ASSUMPTIONS•We’ll 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? Δy = b1 Δx when Δu=0 b1is the slope parameterand captures the ___ 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 + u•wage is an individual hourly wage. •educis an individual years of schooling. •u could include factors like work experience, innate ability etc. •b1 represents the change in the hourly wage associated with an additional year of education when we hold all other factors constant. 1. MODEL: DEFINITIONS & ASSUMPTIONS 1. SLR MODEL: DEFINITIONS & ASSUMPTIONS•In the course of building the simple regression model, we’re going to have to make several assumptions. One of the first assumptions we’ll make is: Assumption 1: The mean value of u in the population is 0....
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lecture%206_s - In-class exercise•There are 5 nobel...

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