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lect10_2010

# lect10_2010 - Introduction to Econometrics Econ 322 Fall...

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1 / 14 Introduction to Econometrics Econ 322 Fall, 2010 Lecture 10: Simple Linear Regression II October 6, 2010

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Topics Covered triangleright Topics Covered The Simple Linear Regression Model Assumptions of the SLRM Assumption 1 Assumptions 2 and 3 Properties of the OLS Estimators The sampling variance of the OLS estimators Summary 2 / 14 1. Assumptions of the SLRM 2. Sampling Distribution of OLS 3. Hypothesis testing 4. Confidence Intervals
The Simple Linear Regression Model Topics Covered triangleright The Simple Linear Regression Model Assumptions of the SLRM Assumption 1 Assumptions 2 and 3 Properties of the OLS Estimators The sampling variance of the OLS estimators Summary 3 / 14 square recall that the simple linear regression model is y i = β 0 + β 1 x i + epsilon1 i square we constructed an estimator for β 0 and β 1 square ˆ β 1 = N i =1 ( x i - x )( y i - y ) N i =1 ( x i - x ) 2 square ˆ β 0 = y - x ˆ β 1

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The SLRM (cont) Topics Covered triangleright The Simple Linear Regression Model Assumptions of the SLRM Assumption 1 Assumptions 2 and 3 Properties of the OLS Estimators The sampling variance of the OLS estimators Summary 4 / 14 square we want to work out the sampling distribution of these estimators square to do so we need to 1. make some simplifying assumptions 2. use these assumptions to derive the sampling properties of the least squares estimators
Assumptions of the SLRM Topics Covered The Simple Linear Regression Model triangleright Assumptions of the SLRM Assumption 1 Assumptions 2 and 3 Properties of the OLS Estimators The sampling variance of the OLS estimators Summary 5 / 14 square to characterize the sampling distribution of the OLS estimators we make the following assumptions: 1. The conditional distribution of epsilon1 given X has mean zero, that is, E ( epsilon1 | X = x

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lect10_2010 - Introduction to Econometrics Econ 322 Fall...

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