Formulas

# Formulas - 2 • If u i ∼ iidN(0,σ 2 ⇒ b β i-β i c...

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ECON 4261: Introduction to Econometrics Fall 2009 Formulas for the Midterm Regression with one explanatory variable Model: Y i = β 1 + β 2 X i + u i Assumptions E ( u i ) = 0 , for all i V ar ( u i ) = σ 2 , for all i cov ( u i ,u j ) = 0 for all i,j Normal equations: n i =1 b u i = 0 and n i =1 X i b u i = 0 b β 2 = n i =1 X i Y i - n X Y n i =1 X 2 i - n X 2 = n i =1 ( X i - X )( Y i - Y ) n i =1 ( X i - X ) 2 = n i =1 ( X i - X ) Y i n i =1 ( X i - X ) 2 = n i =1 X i ( Y i - Y ) n i =1 ( X i - X ) 2 b β 1 = Y - b β 2 X var ( b β 2 ) = σ 2 n i =1 ( X i - X ) 2 b σ 2 = 1 n - 2 n i =1 b u 2 i TSS = n i =1 ( Y i - Y ) 2 ESS = n i =1 ( b Y i - ˆ Y ) 2 RSS = n i =1 ( Y i - b Y i ) 2 = n i =1 b u 2 i R 2 = ESS TSS = 1 - RSS TSS = b β 2 2 n i =1 ( X i - X ) 2 n i =1 ( Y i - Y ) 2 = ± n i =1 ( X i - X )( Y i - Y ) ² 2 n i =1 ( X i - X ) 2 n i =1 ( Y i - Y
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Unformatted text preview: ) 2 • If u i ∼ iidN (0 ,σ 2 ) ⇒ b β i-β i c std ( b β i ) ∼ t ( n-2) i = 1 , 2 Regression with more than one variable • Model: Y i = β 1 + β 2 X 2 i + ... + β k X ki + u i → Y = Xβ + u • Normal equations: X X b β = X Y X b u = 0 • b β = ( X X )-1 X Y • var ( b β ) = σ 2 ( X X )-1 1...
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