Chapter_15

Chapter_15 - Chapter 15 Multiple Regression Model Building...

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Click to edit Master subtitle style 1Chap 15-1 Chapter 15 Multiple Regression Model Building

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2Chap 15-2 n The relationship between the dependent variable and an independent variable may not be linear n Can review the scatter plot to check for non- linear relationships n Example: Quadratic model n The second independent variable is the square of the first variable Nonlinear Relationships i 2 1i 2 1i 1 0 i ε X β X β β Y + + + =
3Chap 15-3 Linear fit does not give random residuals Linear vs. Nonlinear Fit Nonlinear fit gives random residuals X residuals X Y X Y X Obj101

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4Chap 15-4 Quadratic Regression Model Quadratic models may be considered when the scatter plot takes on one of the following shapes: X 1 Y X1 X 1 Y Y Y β1 < 0 β1 > 0 β1 < 0 β1 > 0 β1 = the coefficient of the linear term β2 = the coefficient of the squared term X 1 i 2 1i 2 1i 1 0 i ε X β X β β Y + + + = β2 > 0 β2 > 0 β2 < 0 β2 < 0
5Chap 15-5 Testing the Overall Quadratic Model n Test for Overall Relationship H0: β1 = β2 = 0 (no overall relationship between X and Y) H1: β1 and/or β2 ≠ 0 (there is a relationship between X and Y) n FSTAT = 2 1i 2 1i 1 0 i X b X b b Y ˆ + + = Obj104 n Estimate the quadratic model to obtain the regression equation:

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6Chap 15-6 Testing for Significance: Quadratic Effect n Testing the Quadratic Effect Hypotheses (The quadratic term does not improve the model) (The quadratic term improves the model) n The test statistic is H0: β2 = 0 H1: β2 0 (continued ) 2 b 2 2 STAT S β b t - = 3 n d.f. - = where: b2 = squared term slope coefficient β2 = hypothesized slope (zero) Sb = standard error of the slope 2
7Chap 15-7 Testing for Significance: Quadratic Effect n

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This note was uploaded on 05/31/2011 for the course MGT C06 taught by Professor A.stawinoga during the Fall '10 term at University of Toronto.

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Chapter_15 - Chapter 15 Multiple Regression Model Building...

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