FormulaSheetMidterm

FormulaSheetMidterm - Formula sheet for midterm Classical...

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Unformatted text preview: Formula sheet for midterm Classical Linear Regression (CLR) model The observations Y , i n iK i i X X , , , 1 K n , , 1 K = , on a dependent variable Y and K independent variables satisfy K X X , , 1 K (1) i iK K i i i u X X X Y + + + + = β β β L 2 2 1 1 for . n i , , 1 K = Assumption 1: u are random variables with n i i , , 1 , K = ) ( = i u E Assumption 2: are deterministic, i.e. non-random, constants. K k n i X ik , , 1 , , , 1 , K K = = Assumption 3: (Homoskedasticity) All have the same variance, i.e. for i s u i ' n , , 1 K = (2) 2 2 ) ( ) ( σ = = i i u E u Var Assumption 4 (No serial correlation) The random errors u and are not correlated for all i j u n j i , , 1 K = ≠ (3) ) ( ) , ( = = j i j i u u E u u Cov For the CLR model with normal errors we make the additional assumption: Assumption 5. The random error terms u n i i , , 1 , K = are random variables with a normal distribution. Ordinary Least Squares (OLS) estimators in the simple CLR model and their sampling variance...
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FormulaSheetMidterm - Formula sheet for midterm Classical...

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