725 note 2010_s1_1_linear - 1 LINEAR REGRESSION UNDER IDEAL...

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1 | Linear Regressions under Ideal Conditions (I) 1. LINEAR REGRESSION UNDER IDEAL CONDITIONS (I) What do we learn in this section? [1] Regression model. • What is “regression model”? [2] (Strong) Assumptions. • What assumptions for regression models? • How should a sample be collected from population? [3] Ordinary Least Squares (OLS). • This is the popular estimation method for regression models. [4] Goodness of Fit. • Does your estimated regression model explain your sample well? [5] Statistical Properties of the OLS estimator. • Is the OLS estimator unbiased and normal?
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2 | Linear Regressions under Ideal Conditions (I) What do we learn in this section? Continue… [6] Efficiency. • Is the OLS estimator most reliable estimator? • If so, in what sense? [7] Testing Linear Hypothesis. • How can we test the hypotheses related to regression models? [8] Forecasting. • Can we use our regression results for forecasting? [9] Weaker Assumptions. • Does the OLS estimator have good properties under more realistic circumstances?
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3 | Linear Regressions under Ideal Conditions (I) [1] What is “Regression Model”? • Interested in the average relation between income ( y ) and education ( x ). • For the people with 12 years of schooling ( x =12), what is the average income ( ( | 12) E y x )? • For the people with x years of schooling, what is the average income ( ( | ) E y x )? • Regression model: ( | ) y E y x u , where u is an error term with ( | ) 0 E u x .
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