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Slides_Econ140A_Multiple_Regression

Slides_Econ140A_Multiple_Regression - Goals Properties of a...

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10/20/2011 1 Multiple Regression Copyright Dick Startz 1 Goals Properties of a multiple regression Multicollinearity What makes for a tight estimate of ? in a multiple regression? F- tests Copyright Dick Startz 2 Multiple regression ? ? = ? 1 ? 1? + ? 2 ? 2? + ⋯ + ? ? ? ?? + 𝜀 ? ? right hand side variables. Copyright Dick Startz 3 Multiple Regression Assumptions and results 1. ? ? = ? 1 ? ?1 + ? 2 ? ?2 + ⋯ + ? ? ? ?? + 𝜀 ? , true model of DGP 2. 𝑋 nonrandom (or exogenous), 𝑋 not perfectly collinear 3. ? 𝜀 ? = 0 ∀? Least squares is unbiased ? ? 1 = ? 1 ? ? ? = ? ? Copyright Dick Startz 4 More assumptions and results 4. Homoskedasticity ? 𝜀 ? 𝜀 ? = 𝜎 2 , ? = ? 0, ? ≠ ? There is a (messy) formula for var ? 1 … var ? ? . And for cov ? 1 , ? 2 , cov ? 1 , ? 3 . Gauss-Markov, ? 1 is BLUE, ? 2 is BLUE… Copyright Dick Startz 5 Normality assumption 5. (sometimes) 𝜀~????𝑎? ? is normal In a large sample, ? is asymptotically normal. Copyright Dick Startz 6
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10/20/2011 2 ? 1 in a 2 RHS variable regression ?
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