This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: What is regression? Regression : modelling expectation (or mean or average) Assumes expectation of a single response (or dependent) variable is a function of one or more other variables Important: intent of the regression analysis determines the content of the regression analysis Lecture 2 p. 1/32 Purposes of regression Prediction Covariate selection (variable screening) Model specification Parameter estimation Lect u Simple linear regression Basic, review, but very important Building block for future concepts Can visualize the complete regression problem easily Lecture 2 p. 3/32 The problem Data comes from Example 2.1 in the text Explanatory variable (or covariate of interest) is the accounting rate on a stock (represents input into investment) Dependent variable (or response variable) is the marke t rate (or return) Lect u Accounting data10 10 20 30 40 5 10 15 20 ACCOUNTINGRATE MARKETRATE Lecture 2 p. 5/32 Accounting data Goal: Build a model to predict the market rate using the accounting rate and to make inference about the quantitative nature of their relationship How do we do this? Important: State the model and the assumptions Lect u SLR model Let y be the variable representing the response, x be the variable representing the covariate of interest Simple linear regression assumes y = + 1 x + where is the intercept, 1 is the slope and is the model error Usually index by i = 1 , ..., n , where y i = + 1 x i + i Lecture 2 p. 7/32 Basic assumptions One conditions on the x i values (i.e. we treat x as constant, rather than as a random variable) and assumes the error around the measurement of x is negligible i are uncorrelated random variables with mean E ( i ) = 0 and variance V ar ( i ) = 2 Note: variance does not depend on i or X ! y i are random variables such that: E ( y i  x i ) = + 1 x i V ar ( y i  x i ) = 2 Lect u Centered model Computationally speaking, sometimes useful to center covariates Can write: y i = * + 1 ( x i x ) + i where * = + 1 x Lecture 2 p. 9/32Lecture 2 p....
View
Full
Document
This note was uploaded on 01/15/2010 for the course MATH 423 taught by Professor Steele during the Spring '06 term at McGill.
 Spring '06
 STEELE
 Linear Regression, Regression Analysis

Click to edit the document details