CHAPTER 17 Model building to accompany Introduction to business statistics fourth edition, by Ronald m. Weiers Presentation by Priscilla Chaffe-Stengel Donald N. stengel o The Wadsworth Group
CHAPTER 17 Model Building to accompany Introduction to Business Statistics fourth edition, by Ronald M. Weiers Presentation by Priscilla Chaffe-Stengel Donald N. Stengel © 2002 The Wadsworth Group
l Chapter 17-learning objectives Build polynomial regression models to describe curvilinear relationships Apply qualitative variables representing two or three categories Use logarithmic transforms in constructing exponential and multiplicative models Identify and compensate for multicollinearity apply stepwise regression Select the most suitable among competing models o 2002 The Wadsworth Group
Chapter 17 - Learning Objectives • Build polynomial regression models to describe curvilinear relationships • Apply qualitative variables representing two or three categories. • Use logarithmic transforms in constructing exponential and multiplicative models. • Identify and compensate for multicollinearity • Apply stepwise regression • Select the most suitable among competing models © 2002 The Wadsworth Group
l Polynomial models with One Quantitative predictor variable Simple linear regression equation =tbx Equation for second-order polynomial model y=b+6x+b,x Equation for third-order polynomial model b.+ tb.x Equation for general polynomial model: y=6+bx+6x+bx'+.+bxp o 2002 The Wadsworth Group
Polynomial Models with One Quantitative Predictor Variable • Simple linear regression equation: • Equation for second-order polynomial model: • Equation for third-order polynomial model: • Equation for general polynomial model: © 2002 The Wadsworth Group y b b x 0 1 ˆ = + 2 0 1 2 y ˆ = b + b x + b x 3 3 2 0 1 2 y ˆ = b + b x + b x + b x p p y ˆ = b + b x + b x + b x + ...+ b x 3 3 2 0 1 2
l Polynomial models with Two Quantitative predictor variables First-order model with no interaction 6+6,x+b,x2 First-order model with interaction y=6+b,,+ b,x,+b,, x, Second-order model with no interaction y=6 +bx+b,x,+bx,+ bx Second-order model with interaction: i=b+b,,+bx+6x f+6x+bx o 2002 The Wadsworth Group
Polynomial Models with Two Quantitative Predictor Variables • First-order model with no interaction: • First-order model with interaction: • Second-order model with no interaction: • Second-order model with interaction: © 2002 The Wadsworth Group 0 1 1 2 2 y ˆ = b + b x + b x 0 1 1 2 2 3 1 2 y ˆ = b + b x + b x + b x x 2 4 2 2 0 1 1 2 2 3 1 y ˆ = b + b x + b x + b x + b x 5 1 2 2 4 2 2 0 1 1 2 2 3 1 y ˆ = b +b x +b x +b x +b x +b x x
l Models with qualitative variables Equation for a model with a categorical independent variable with two possible states D=6+b,x where state 1 is shown=1 where state 2 is shown x=0 Equation for a model with a categorical independent variable with three possible states y=b+b,x,+b,x where state 1 is shown,=1x=0 where state 2 is shown x1=0, x2=1 Where state 3 is shown x,=0,x=0 o 2002 The Wadsworth Group
Models with Qualitative Variables • Equation for a model with a categorical independent variable with two possible states: – where state 1 is shown x = 1 – where state 2 is shown x = 0 • Equation for a model with a categorical independent variable with three possible states: – where state 1 is shown x1 = 1, x2 = 0 – where state 2 is shown x1 = 0, x2 = 1 – Where state 3 is shown x1 = 0, x2 = 0 © 2002 The Wadsworth Group y b b x 0 1 ˆ = + 0 1 1 2 2 y ˆ = b + b x + b x