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POL322 Lecture #8 .docx

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Political Science

10/4/13 POL332 Lecture #8 Modeling the Relationship between two or more variables Bivariate & multivariate linear regression Statistical Inference - Descriptive inference 1. Point estimation 2. Interval estimation 3. Hypothesis testing - Statistical Inference o Causal Inference o Associational Inference Linear Regression Model Modeling the Relationship between Variables 1. Bivariate Regression Model - Population model - Estimation Example: Economic Voting in U.S. 2. Multivariate Regression - Population Model - Estimation Example: Forecasting U.S. Pres. Elections Population Model: Descriptive Inference (Y only) - Cannot afford to study everyone in the population, therefore we use a random sample o Therefore the population dist of Y = probability dist of Y o Population dist of continuous variable we use density Population Model: Linear Regression (X & Y) - 3 dimensional histogram - Again, cannot afford to study everything, therefore we use a random sample of X, Y o Population Dist of X & Y = Joint Probability of X & Y Population: Joint Prob Dist of X & Y, p(X,Y) - the height represents density - Conditional expectation of Y given the value of X - The value of Y we expect, given the certain value of X Probabilistic Relationship between X & Y - The causal relationship we expect in social science is almost always probabilistic - The red line represents the probability of having a X, Y combination is high, away from the red line is relatively small Population - a = intercept: the value of E(YlX) when x= 0 - b = slope: the value of change in E(YlX) when X changes in one unit o conditional expectation when X changes in one unit, Y will ch
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