Chap14-SSM - 354 Chapter 14: Introduction to Multiple...

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Unformatted text preview: 354 Chapter 14: Introduction to Multiple Regression CHAPTER 14 OBJECTIVES To learn how to develop a multiple regression model To know how to interpret the regression coefficients To learn how to determine which independent variables to include in the regression model To know how to determine which independent variables are more important in predicting a dependent variable To be able to use categorical variable in regression models OVERVIEW AND KEY CONCEPTS The Multiple Regression Model The multiple regression model describes the relationship between one dependent variable and 2 or more independent variables in a linear function. The Simple Linear Regression and Multiple Regression Compared Coefficients in a simple regression pick up the impact of that variable plus the impacts of other variables that are correlated with it and the dependent variable. Coefficients in a multiple regression net out the impacts of other variables in the equation. Hence, they are called net regression coefficients . Interpretation of the Estimated Coefficients The Y intercept ( ) b : The estimated average value of i Y when all i X = . Slope ( ) i b : Estimated that the average value of Y changes by i b for each one-unit increase in i X holding constant the effect of all other independent variables. Predicting the Dependent Variable Y Use the estimated sample regression equation (multiple linear regression equation): 1 1 i i k k i Y b b X b X = + + + L 1 1 2 2 i i i k k i i Y b b X b X b X e = + + + + + L Population Y-intercept Population slopes Random Error Dependent (response) variable Independent (explanatory) variables 1 2 i i i k k i i Y X X X 1 2 = + + + + + L Residual Study Guide and Students Solutions Manual 355 The Venn Diagram and Explanatory Power of the Multiple Regression Model Coefficient of Multiple Determination Coefficient of multiple determination measures the proportion of total variation in Y explained by all X variables taken together. 2 12 Explained Variation Total Variation Y k SSR r SST = = L It never decreases when an additional X variable is added to the model, which is a disadvantage when comparing among models. Y X 1 2 r SSR SSR SSE = = + Y X 1 Variations in Y explained by X 1 or variations in X 1 used in explaining variation in Y Variations in Y not explained by X 1 Variations in X 1 not used in explaining variation in Y ( ) SSE ( ) SSR Y X 1 X 2 Overlapping Overlapping variation in both X 1 and X 2 are used in explaining the variation variation in Y but NOT NOT in the estimation estimation of nor 1 2 Variation NOT NOT explained by X 1 nor X 2 ( ) SSE 356 Chapter 14: Introduction to Multiple Regression Adjusted Coefficient of Multiple Determination It measures the proportion of variation in Y explained by all X variables adjusted for the number of X variables used....
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Chap14-SSM - 354 Chapter 14: Introduction to Multiple...

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