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Unformatted text preview: 1 School of Business and Economics SUNY Plattsburgh Slide 1 Business Statistics II ECO 362: Sections A & B Chapter 16 Regression Analysis: Model Building Spring 2011 Dr. Kameli a Petrova Spring 2011 Dr. Kameli a Petrova School of Business and Economics SUNY Plattsburgh Slide 2 Regression Analysis: Model Building s Multiple Regression Approach to Analysis of Variance and Experimental Design s General Linear Model s Determining When to Add or Delete Variables s Variable Selection Procedures s Residual Analysis Spring 2011 Dr. Kameli a Petrova School of Business and Economics SUNY Plattsburgh Slide 3 s Linear models: models in which all parameters ( , 1 , . . . , p ) have exponents of one. General Linear Model s General linear model with p independent variables: = + + + + + L 1 1 2 2 p p y z z z s Each of the independent variables z is a function of x 1 , x 2 ,..., x k (the variables for which data have been collected). Spring 2011 Dr. Kameli a Petrova School of Business and Economics SUNY Plattsburgh Slide 4 General Linear Model y x = + + 1 1 y x = + + 1 1 s The simplest case is when z 1 = x 1 . We want to estimate y by using a straightline relationship. s Simple firstorder model with one predictor (independent) variable. Spring 2011 Dr. Kameli a Petrova School of Business and Economics SUNY Plattsburgh Slide 5 Modeling Curvilinear Relationships s Secondorder model with one predictor variable: y x x = + + + 1 1 2 1 2 y x x = + + + 1 1 2 1 2 s To account for a curvilinear relationship we set z 1 = x 1 and z 2 = x 1 2 Spring 2011 Dr. Kameli a Petrova School of Business and Economics SUNY Plattsburgh Slide 6 Interaction y x x x x x x = + + + + + + 1 1 2 2 3 1 2 4 2 2 5 1 2 y x x x x x x = + + + + + + 1 1 2 2 3 1 2 4 2 2 5 1 2 s This type of effect is called interaction . s Variable z 5 = x 1 x 2 is added to account for the potential effects of the two variables acting together. s Secondorder model with two predictor variables. 2 Spring 2011 Dr. Kameli a Petrova School of Business and Economics SUNY Plattsburgh Slide 7 Transformations Involving the Dependent Variable s Reciprocal transformation: use 1/ y as the dependent variable instead of y . s The nonconstant variance can be corrected by transforming the dependent variable to a different scale. s Logarithmic transformations: using either the base10 (common log) or the base e = 2.71828... (natural log). Log(y) or Ln(y) instead of y Spring 2011 Dr. Kameli a Petrova School of Business and Economics SUNY Plattsburgh Slide 8 s Transform to a linear model by taking the logarithm of both sides. E y x ( ) = 1 E y x ( ) = 1 Nonlinear Models That Are Intrinsically Linear s Models in which the parameters ( , 1 , . . . , p ) have exponents other than one are called nonlinear models ....
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