class2-642-08

Class2-642-08 - Econ 642 Monday March 24 class 1 Econ 642 Wednesday March 26 class 2 Robert de Jong 1 1 Department of Economics Ohio State

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Unformatted text preview: Econ 642, Monday March 24, class 1 Econ 642, Wednesday March 26, class 2 Robert de Jong 1 1 Department of Economics Ohio State University Robert de Jong Econ 642, Wednesday March 26, class 2 Econ 642, Monday March 24, class 1 Model and Least squares principle Interpretation of coefficients Software, taking logarithms, and R 2 Inference and GRE example Model assumptions Outline 1 Econ 642, Monday March 24, class 1 Model and Least squares principle Interpretation of coefficients Software, taking logarithms, and R 2 Inference and GRE example Model assumptions Robert de Jong Econ 642, Wednesday March 26, class 2 Econ 642, Monday March 24, class 1 Model and Least squares principle Interpretation of coefficients Software, taking logarithms, and R 2 Inference and GRE example Model assumptions Simple regression: estimates model y i = β + β 1 x i + u i Multiple regression: estimates model y i = β + β 1 x i 1 + . . . + β k x ik + u i Interpretation of β j : β j is the amount with which E ( y i | x i 1 , . . . , x ik ) increases if x ij goes up by one unit, keeping all other variables constant Robert de Jong Econ 642, Wednesday March 26, class 2 Econ 642, Monday March 24, class 1 Model and Least squares principle Interpretation of coefficients Software, taking logarithms, and R 2 Inference and GRE example Model assumptions Least Squares principle - simple regression Minimizing n summationdisplay i = 1 ( y i- ( β + β 1 x i )) 2 over all possible values of β and β 1 gives ˆ β 1 = n · ∑ n i = 1 x i y i- ∑ n i = 1 x i · ∑ n i = 1 y i n · ∑ n i = 1 x 2 i- ( ∑ n i = 1 x i ) 2 and ˆ β = ¯ y- ˆ β 1 ¯ x . Note ¯ y = n- 1 ∑ n i = 1 y i , the average of the y i The mathematical calculation requires being able to find the minimum of a function of two variables using differentiation Robert de Jong Econ 642, Wednesday March 26, class 2 Econ 642, Monday March 24, class 1 Model and Least squares principle Interpretation of coefficients Software, taking logarithms, and R 2 Inference and GRE example Model assumptions Least squares principle - multiple regression minimize n summationdisplay i = 1 ( y i- ( β + β 1 x i 1 + . . . + β k x ik )) 2 This problem can be solved using matrix algebra Robert de Jong Econ 642, Wednesday March 26, class 2 Econ 642, Monday March 24, class 1 Model and Least squares principle Interpretation of coefficients Software, taking logarithms, and R 2 Inference and GRE example Model assumptions Outline 1 Econ 642, Monday March 24, class 1 Model and Least squares principle Interpretation of coefficients Software, taking logarithms, and R 2 Inference and GRE example Model assumptions Robert de Jong Econ 642, Wednesday March 26, class 2 Econ 642, Monday March 24, class 1 Model and Least squares principle Interpretation of coefficients Software, taking logarithms, and R 2 Inference and GRE example Model assumptions Interpretation of coefficients We obtain the regression line y = ˆ β + ˆ β 1 x y i : demand for housing of individual # i, in dollars annually...
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This note was uploaded on 07/17/2008 for the course ECON 642 taught by Professor De jong during the Spring '08 term at Ohio State.

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Class2-642-08 - Econ 642 Monday March 24 class 1 Econ 642 Wednesday March 26 class 2 Robert de Jong 1 1 Department of Economics Ohio State

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