Chapter 14 Notes

Chapter 14 Notes - Chapter 14 Simple Linear Regression...

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Unformatted text preview: Chapter 14 Simple Linear Regression Outline: • Simple Linear Regression Model • Least Squares Method • Coefficient of Determination • Model Assumptions • Testing for Significance • Using the Estimated Regression Equation for Estimation and Prediction • Residual Analysis: Validating Model Assumptions What is regression for? • Describe the relationship between a response/dependent variable and at least one exploratory/independent variable. • Used for prediction e.g., Sales versus promotion activities • Correlation Analysis – Measures the association of numerical values – e.g., Euro and U.S. dollars 1 POLAROID CORPORATION • Polaroid uses Regression Analysis to produce films with the performance levels its customers desire: $ $ 19.8 7.6 = change in film Speed x = film age in months *Average decrease in film speed =_____units/months y x Where y = -- The Simple Linear Regression Model The Simple Linear Regression Model: Simple Linear Regression Model y = β + β 1 x + ε (randomness) Simple Linear Regression Equation E( y ) = β + β 1 x Estimated Simple Linear Regression Equation y ˆ = b + b 1 x (propagated randomness) 2 Least Squares Method: Error or Residual: i i i Y Y e ˆ- = Least Squares Criterion: Minimize the sum of squared errors. min ∑ =- n i i i y y 1 2 ) ˆ ( = min ∑ = n i i e 1 2 ) ( where: i y = observed value of the dependent variable for the i th observation i y ˆ = estimated value of the dependent variable for the i th observation Least Square Estimators: • Sum of squares and cross products: e 2 e 1 e 3 e 4 Y X i i X b b Y 1 ˆ + = 3 ( 29 ( 29 ( 29 ( 29 n y x y x y y x x SS n y y y y SS n x x x x SS i i i i i i XY i i i Y i i i X ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑- =-- =- =- =- =- = ) )( ( ) ( ) ( 2 2 2 2 2 2 • Regression estimators: The Least Squares Method: Slope for the Estimated Regression Equation y-Intercept for the Estimated Regression Equation x b y b 1- = where: i x = value of independent variable for i th observation i y = value of dependent variable for i th observation x = mean value for independent variable y = mean value for dependent variable n = total number of observations 4 ∑ ∑ ∑ ∑ ∑ ∑ ∑-- =--- = n x x n y x y x x x y y x x b i i i i i i i i i / ) ( / ) ( ) ( ) )( ( 2 2 2 1 x b y b SS SS b X XY 1 1- = = Example:...
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This note was uploaded on 12/06/2011 for the course MGMT 305 taught by Professor Priya during the Fall '08 term at Purdue.

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Chapter 14 Notes - Chapter 14 Simple Linear Regression...

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