This preview shows pages 1–8. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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...
View
Full
Document
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.
 Spring '08
 DE JONG
 Economics

Click to edit the document details