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Multivariate Regression

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  Multivariate Regression  Introduction ã The population regression model of a dependent variable, Y  , on a set of k  independent variables,  X  1 ,  X  2 ,. . . ,  X  k  is given by: Y = β 0 + β 1 X 1 + β 2 X 2 + β 3 X 3 + . . . + β k X k + ε Y = the value of the dependent (response) variable β 0 = the regression constant β 1 = the partial regression coefficient of independent variable 1 β 2 = the partial regression coefficient of independent variable 2 β k = the partial regression coefficient of independent variable k k = the number of independent variables ε = the error of prediction  Model Assumptions 1.  ε ~ N(0, σ 2 ), independent of other errors.2.The variables  X  i  are uncorrelated with the error term.  Simple and Multiple Least-Squares Regression In a simple regression model , the least-squares estimators minimize the sum of squared errors from the estimated regression line .In a multiple regression model , the least-squares estimators minimize the sum of squared errors from the estimated regression plane . XY x2x1y ˆ 0 1  y b b x     y b b x b x    0 1 1 2 2

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Sep 10, 2019
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