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Linear_regression_Multiple_Regressors

# Linear_regression_Multiple_Regressors - Multiple Regression...

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Multiple Regression Specification of a multiple regression model: Model: i ki k i i i u x x x y + + + + + = β β β β ... 2 2 1 1 0 Note: a total of (k+1) parameters needs to be estimated; hence, the number of degrees of freedom is n-(k+1). Interpretation of Coefficients: Model: i ki k i i i u x x x y + + + + + = β β β β ... 2 2 1 1 0 0 β is the intercept i.e. the value of the dependent variable when ALL INDEPENDENT VARIABLES ARE ZERO k β β β ,..., , 2 1 are partial slope coefficients. For example, 2 β is the partial slope coefficient for x2 meaning that it indicates the effect of a 1-unit change in x2 on the dependent variable (y), holding constant all the other independent variables (x3,x4, …,xk). In econometrics, holding constant (x3,x4,…,xk) is also referred to as controlling for (x3,x4,…,xk). Model: i ki k i i i u x x x y + + + + + = β β β β ... 2 2 1 1 0 Assumptions: 1. Zero mean : 0 ) ,..., / ( 2 , 1 = ki i i i x x x u E 2. Constant variance (homoskedasticity) : 2 2 , 1 ) ,..., / ( σ = ki i i i x x x u Var (Constant value). Violation of this assumption is called heteroskedasticity i.e.

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