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lecture+6_complete

# lecture+6_complete - In-class exercise The accompanying...

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In-class exercise The accompanying table shows the joint distribution between an individual’s 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 0 Y 1 Y 0 X 1 X

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Questions 1. Compute E(X) and interpret the result. 2. Calculate and interpret E(Y|X=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 0 + b 1 x + u The Simple Regression Model

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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 & ASSUMPTIONS y 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.

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1. SLR MODEL: DEFINITIONS & ASSUMPTIONS We’ll resolve all three issues by writing the following equation: y = b 0 + b 1 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 & ASSUMPTIONS

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1. SLR MODEL: DEFINITIONS & ASSUMPTIONS y = b 0 + b 1 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 y and x. If the other factors in u are held fixed, so that the change in u is zero ( Δ u=0), then: Δy = b 1 Δ x when Δ u=0 b 1 is the slope parameter and captures the ceteris paribus (causal )effect of x on y. b 0 is 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 = b 0 + b 1 educ + u wage is an individual hourly wage. educ is an individual years of schooling.

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lecture+6_complete - In-class exercise The accompanying...

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