15_regression

# 15_regression - Regression Lecture 15 STAT 651 Survey...

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Regression Lecture 15 STAT 651: Survey Sampling Methods, Kaizar – p.1/12

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Lecture 15: Regression Reading: Lohr Chapter 11 Motivating Example Introduction to Regression Usual Regression Estimates Regression in the Design Setting STAT 651: Survey Sampling Methods, Kaizar – p.2/12
Motivating Example Is the respondent’s age related to the respondents’ spouse’s age? STAT 651: Survey Sampling Methods, Kaizar – p.3/12

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Linear Regression in a Nutshell Assume the following model: Y i | x i = β 0 + β 1 x i + ǫ i E ( ǫ i ) = 0 V ( ǫ i ) = σ 2 Cov ( ǫ i , ǫ j ) = 0 Goal: Estimate β 0 and β 1 . STAT 651: Survey Sampling Methods, Kaizar – p.4/12
Least Squares Estimate ˆ β 1 = i ( y i - ¯ y ) ( x i - ¯ x ) i ( x i - ¯ x ) 2 ˆ β 0 = ¯ y - ˆ β 1 ¯ x ˆ V parenleftBig ˆ β 1 parenrightBig = i ǫ 2 i / ( n - 2) ( x i - ¯ x ) 2 = i parenleftBig y i - ˆ β 0 - ˆ β 1 x i parenrightBig 2 / ( n - 2) ( x i - ¯ x ) 2 STAT 651: Survey Sampling Methods, Kaizar – p.5/12

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Finite Population Setting B 1 = summationdisplay i ∈S ( y i - ¯ y U ) ( x i - ¯ x U ) summationdisplay i ∈S ( x i - ¯
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