Appendix 2A. Simple regression and multiple regression

By Cheng Few Lee Joseph Finnerty John Lee Alice C Lee Donald Wort Appendix 2A. Simple regression and multiple regression

Appendix 2A. Simple regression and multiple regression 2. A.1 INTRODUCTION 2. A.2 SIMPLE REGRESSION Variance of Multiple Regression

Appendix 2A. Simple regression and multiple regression (2.A.1a) (2.A.1b) (2.A.2a) (2.A.2b)

Appendix 2A. Simple regression and multiple regression (2.A.3) (2.A.4) (2.A.5a) (2.A.5b)

Appendix 2A. Simple regression and multiple regression (2.A.6a) (2.A.6b)

Appendix 2A. Simple regression and multiple regression (2.A.7) (2.A.7a)

Appendix 2A. Simple regression and multiple regression (2.A.8) (2.A.8a)

Variance of Equation (2.A.7a) implies that: (2.A.7b) Where

Variance of (2.A.7c) (2.A.9)

Variance of

Variance of (2.A.10) (2.A.11) (2.A.12)

Multiple Regression (2.A.13a) The error sum of squares can be defined as: Where

Multiple Regression (2.A.14a) (2.A.14b) (2.A.14c)

Multiple Regression 0 = na + b(0) + c(0), (2.A.15a) (2.A.15b) (2.A.15c)

Multiple Regression (2.A.16a) (2.A.16b) (2.A.17)

Multiple Regression (2.A.13b) (2.A.18) (2.A.19)

Multiple Regression (2.A.20) where TSS = Total sum of squares; ESS = Residual sum of squares; and RSS = Regression sum of squares.

Multiple Regression (2.A.21) (2.A.22) Where and k = the number of independent variables.

Multiple Regression (2.A.23) where F(k-1, n-k) represents F-statistic with k－1 and n－k degrees of freedom.

By Cheng Few Lee Joseph Finnerty John Lee Alice C Lee Donald Wort Appendix 2B. Instrumental variables and two-stage least squares

Appendix 2B. Instrumental variables and two-stage least squares 2. B.1 ERRORS-IN-VARIABLE PROBLEM 2. B.2 INSTRUMENTAL VARIABLES 2. B.3 TWO-STAGE, LEAST-SQUARE

2. B.1 ERRORS-IN-VARIABLE PROBLEM (2.B.1) (2.B.2) (2.B.3)

2. B.1 ERRORS-IN-VARIABLE PROBLEM (2.B.4) (2.B.5)

2. B.2 INSTRUMENTAL VARIABLES (2.B.6) (2.B.7) (2.B.8a) (2.B.8b)

2. B.2 INSTRUMENTAL VARIABLES (2.B.9a) (2.B.9b) (2.B.10a) (2.B.10b)

2.B.3 TWO-STAGE, LEAST-SQUARE (2.B.11a) (2.B.11b) (2.B.10′a) (2.B.10′b)

2.B.3 TWO-STAGE, LEAST-SQUARE (2.B.12a) (2.B.12b)

Appendix 2A. Simple regression and multiple regression