Section 4 - Section4-EconL40 GSI: Edson Severnini 4.3 The

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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
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Section 4 - Section4-EconL40 GSI: Edson Severnini 4.3 The

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