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Chapter 16 - Business Statistics II ECO 362 Sections A B...

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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. Kameliia Petrova Spring 2011 Dr. Kameliia Petrova School of Business and Economics SUNY Plattsburgh Slide 2 Regression Analysis: Model Building square6 Multiple Regression Approach to Analysis of Variance and Experimental Design square6 General Linear Model square6 Determining When to Add or Delete Variables square6 Variable Selection Procedures square6 Residual Analysis Spring 2011 Dr. Kameliia Petrova School of Business and Economics SUNY Plattsburgh Slide 3 square6 Linear models: models in which all parameters ( β 0 , β 1 , . . . , β p ) have exponents of one. General Linear Model square6 General linear model with p independent variables: β β β β ε = + + + + + L 0 1 1 2 2 p p y z z z square6 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. Kameliia Petrova School of Business and Economics SUNY Plattsburgh Slide 4 General Linear Model y x = + + β β ε 0 1 1 x β 0 1 1 square6 The simplest case is when z 1 = x 1 . We want to estimate y by using a straight-line relationship. square6 Simple first-order model with one predictor (independent) variable . Spring 2011 Dr. Kameliia Petrova School of Business and Economics SUNY Plattsburgh Slide 5 Modeling Curvilinear Relationships square6 Second-order model with one predictor variable: y x x = + + + β β β ε 0 1 1 2 1 2 y x x = + + + β β β ε 1 square6 To account for a curvilinear relationship we set z 1 = x 1 and z 2 = x 1 2 Spring 2011 Dr. Kameliia Petrova School of Business and Economics SUNY Plattsburgh Slide 6 Interaction y x x x x x x = + + + + + + β β β β β β ε 0 1 1 2 2 3 1 2 4 2 2 5 1 2 y x x = + + β β 2 2 3 1 square6 This type of effect is called interaction . square6 Variable z 5 = x 1 x 2 is added to account for the potential effects of the two variables acting together. square6 Second-order model with two predictor variables .
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2 Spring 2011 Dr. Kameliia Petrova School of Business and Economics SUNY Plattsburgh Slide 7 Transformations Involving the Dependent Variable square6 Reciprocal transformation: use 1/ y as the dependent variable instead of y . square6 The non-constant variance can be corrected by transforming the dependent variable to a different scale. square6 Logarithmic transformations: using either the base-10 (common log) or the base e = 2.71828... (natural log). Log(y) or Ln(y) instead of y Spring 2011 Dr. Kameliia Petrova School of Business and Economics SUNY Plattsburgh Slide 8 square6 Transform to a linear model by taking the logarithm of both sides. E y x ( ) = β β 0 1 ( β β Nonlinear Models That Are Intrinsically Linear square6 Models in which the parameters ( β 0 , β 1 , . . . , β p ) have exponents other than one are called nonlinear models .
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