# ch_14_Notes - Chapter 14 Simple Linear Regression Outline:...

This preview shows pages 1–9. Sign up to view the full content.

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

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

View Full Document
Steps of Regression Modeling: Define problem Specify model: for example, y = βx + ε Collect Data: ((x 1 , y 1 ), (x 2 , y 2 ), … (x n , y n )) Descriptive Data Analysis Estimate unknown parameters Evaluate Model Use Model for prediction Step 1: Define Problem What are the model objectives? Who will use the model? What are the benefits? Are resources available (data)? How will the results be implemented? Example: Develop a model to explain the variations in sales by advertising and promotional activities. 2
Step 2: Specify Model-- Which is logical? Simple Linear Regression Models Widely used for trends analysis One dependent variable ( i y is the dependent variable) One independent variable ( i x is independent/exploratory variable) 3 Advertising Sale s Advertising Sales Advertising Sales Advertising Sales Y Y  =  mX  +  b X m  = Slope b   Y -intercept

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

View Full Document
Three possible regression lines in simple linear regression (Figure 14.1 ASW). 4
Step 3: Collect Data Step 4: Descriptive Data Analysis Scatter Diagram Correlation Coefficient Example: 5 Population \$ \$ \$ \$ Unknown  Relationship ε β + + = X Y 1 0 Random Sample \$ \$ \$ \$ e X b b Y + + = 1 0 promotion versus sales 80 85 90 95 100 105 110 115 120 125 80 85 90 95 100 105 110 115 120 promotion sales

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

View Full Document
Correlation Coefficients: Linear association between variables The Simple Linear Regression Model: Simple Linear Regression Model y = β 0 + 1 x + ε (randomness) Simple Linear Regression Equation E( y ) = 0 + 1 x Estimated Simple Linear Regression Equation y ˆ = b 0 + b 1 x (propagated randomness) The estimated process in simple linear regression (Figure 14.2 ASW). Y X r  = 0 Y X r  = 0 Y X r  = -1 Y X r  = 1 6
Step 5: Estimate Unknown Parameters 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 Why squares? e 2 e 1 e 3 e 4 Y X i i X b b Y 1 0 ˆ + = 7

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

View Full Document
Least Square Estimators: Sum of squares and cross products: Regression estimators: Slope for the Estimated Regression Equation y -Intercept for the Estimated Regression Equation x b y b 1 0 - = where: Y X 8 - - = - - - = 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 ( 29 ( 29 ( 29 ( 29 n y
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 01/31/2011 for the course MGMT 305 taught by Professor Priya during the Spring '08 term at Purdue University-West Lafayette.

### Page1 / 26

ch_14_Notes - Chapter 14 Simple Linear Regression Outline:...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online