Chap13-SSM - 326 Chapter 13: Simple Linear Regression...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
326 Chapter 13: Simple Linear Regression CHAPTER 13 OBJECTIVES To use regression analysis to predict the value of a dependent variable based on an independent variable To understand the meaning of the regression coefficient b 0 and b 1 To be familiar with the assumptions of regression analysis, how to evaluate the assumptions, and what to do if the assumptions are violated To be able to make inferences about the slope and correlation coefficient To be able to estimate mean values and predict individual values OVERVIEW AND KEY CONCEPTS Purpose of Regression Analysis Regression analysis is used for predicting the values of a dependent (response) variable based on the value of at least one independent (explanatory) variable. The Simple Linear Regression Model The relationship between the dependent variable ( ) Y and the explanatory variable () X is described by a linear function. The change of the explanatory variable causes the explained (dependent) variable to change. The value of the explained variable depends on the explanatory variable. The population linear regression: 01 ii i YX β βε = ++ where 0 is the intercept and 1 is the slope of the population regression line |0 1 i X µ ββ = + and i ε is called the error term. The parameters 0 and 1 are unknown and need to be estimated. The least squares estimates for 0 and 1 are 0 b and 1 b , respectively, obtained by minimizing the sum of squared residuals, 2 2 11 nn i Yb b X e == −+ = . i =+ + = Random Error Observed Value of Observed Value of | i X µβ i 0 1 (Conditional Mean) Y Y X
Background image of page 1

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

View Full DocumentRight Arrow Icon
Study Guide and Student’s Solutions Manual 327 The sample linear regression: 01 ii i Ybb Xe = ++ where 0 b is the intercept and 1 b is the slope of the simple linear regression equation ˆ i X =+ and i e is called the residual. The simple linear regression equation (sample regression line) ˆ i X can be used to predict the value of the dependent variable for a given value of the independent variable X . Interpretations of 0 β , 1 , 0 b and 1 b () |0 YX EY X βµ 0= == = is the average value of Y when the value of X is zero. ˆ bE Y X 0 ˆ (0 ) is the estimated average value of Y when the value of X is zero. | 1 change in change in | change in change in X X µ measures the change in the average value of Y as a result of a one-unit change in X . 1 ˆ ˆ change in | change in change in change in Y b X X measures the estimated change in the average value of Y as a result of a one-unit change in X . Some Important Identities in the Simple Linear Regression Model | i Y X i βε ε + = + . The value of the dependent variable is decomposed into the value on the population regression line and the error term. ˆ i i i XeYe =+ +=+ . The value of the dependent variable is decomposed into the value on the sample regression line (fitted regression line) and the residual term.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/26/2012 for the course MATH 104 taught by Professor Green during the Spring '10 term at Golden Gate.

Page1 / 28

Chap13-SSM - 326 Chapter 13: Simple Linear Regression...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online