Chapter 14 Notes

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

This preview shows pages 1–5. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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:...
View Full Document

## This note was uploaded on 12/06/2011 for the course MGMT 305 taught by Professor Priya during the Fall '08 term at Purdue.

### Page1 / 21

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

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online