Lab6_Multilinear Regression_Variable diagnostics

Lab6_Multilinear Regression_Variable diagnostics - EXST...

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EXST 7015 - Statistical Inference II, Fall 2011 Lab 6: Multiple Linear Regression_Variable diagnostics OBJECTIVES In multiple regression however, a number of variables can be involved and regressed on one another (model: Y = β 0 + β 1 X1+ β 2 X2+ · · · + β p XP + ε ) .The overall test of hypothesis of multiple linear regression is H 0 : β 1 = β 2 = · · ·= β p =0 v.s. H 1 : at least one β 0. Rejection of H 0 implies that at least one of the regressors, X1, X2, . . . , Xp, contributes significantly to the model. In the lab5, the problem of multicollinearity caused by highly correlated variables was introduced by indentify the diagnostic statistics of sequential parameter estimates, simple correlation, variance inflation factor (VIF) and condition index. In this lab, an extreme case of muticolinearlity will be presented to help you fully understand those statistics. Since there are more than one independent variables in the model of multiple linear regression, many of you have raised the question that which variables are more important than the others. By using partial SS F-test (Type II, III, IV) and t-test of regression coefficients, the larger the F- value or t-value (the smaller the P-value), the more significant of the variable to the model as you might be aware in lab5. In addition, standardized regression coefficients and partial R^2 will be discussed to help you evaluate the relative importance of individual variables in the model in this lab. Some of you might realize that the absolute value of regression coefficient is not a good predictor of relative importance of the variables. Why it happens is that, most often, the variables are not on the same scale or are of arbitrary scale, which leads to un-meaningful slope (Y units per X units). In such cases, the variables could be standardized with a mean=0 and variance=1.
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This note was uploaded on 12/29/2011 for the course EXST 7015 taught by Professor Wang,j during the Fall '08 term at LSU.

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Lab6_Multilinear Regression_Variable diagnostics - EXST...

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