Section 4

# Section 4 - Section4-EconL40 GSI Edson Severnini 4.3 The in...

This preview shows pages 1–2. Sign up to view the full content.

Section4-EconL40 GSI: Edson Severnini APPENDIX 4.3 The Multiple Regression Model in Matrix Form REPRESENTATION OF THE MULTIPLE REGRESSION MODEL The purpose of this appendix is to present generalizations of important textual items. It would be difficult to accomplish this without using matrix algebra. We presume that the reader has such prior knowledge. We begin by representing the linear model in matrix form. Recall from the text that the regression model includes k + I variables-a dependent variable and k independent variables (including the constant term). Since there are N ' observations, we can summarize the regression model by writing a series of Nl equations, as follows: Yt : Ft * FrXzt + B3X\ + Yz : Ft * FzXzz + B3Xt2 + * B2rXp1 * e1 * BpX2r2 * e2 Yx: Ftl- FzXzN* FtXtx + "'* BkXkTt* eN The corresponding matrix formulation of the model is Y:XF*e in which (44.4) (A4.5) (44.61 [i i}, il':[;;] " [:l I I lx I :NX :NX :kx :NX ":[il where Y x p E I column vector of dependent variable observations k matrix of independent variable observations I column vector of unknown parameters I column vector of errors In our representation of the matrix X, each component {i has two subscripts, i the first signifying the appropriate column (variable) and the second signifying the appropriate row (observation). Each column of X represents a vector of N r observations on a given variable, with all observations associated with the intercept equal to L The assumptions of the classical linear regression model can be represented' as follows: i. The model specification

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 6

Section 4 - Section4-EconL40 GSI Edson Severnini 4.3 The in...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online