Transcription of Chapter 3 Multiple Linear Regression Model The linear model
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Chapter 3 Multiple Linear Regression Model The linear model
Regression Analysis | Chapter 3 | Multiple Linear Regression Model | Shalabh, IIT Kanpur 1 1 1 Chapter 3 Multiple Linear Regression Model We consider the problem of Regression when the study variable depends on more than one explanatory or independent variables, called a Multiple Linear Regression Model . This Model generalizes the simple Linear Regression in two ways. It allows the mean function ()Ey to depend on more than one explanatory variables and to have shapes other than straight lines, although it does not allow for arbitrary shapes. The Linear Model : Let y denotes the dependent (or study) variable that is linearly related to k independent (or explanatory) variables 12.
The normal equation is () 0 '' S X Xb X y where the following result is used: Result: If f 'zZAZ is a quadratic form, Z is a m 1 vector and A is any mm symmetric matrix then Fz Az() 2 z . Since it is assumed that rank()X k (full rank), then X 'X is a positive definite and unique solution of the normal equation is bXX Xy (') ' 1
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