15_regression

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

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Unformatted text preview: Regression Lecture 15 STAT 651: Survey Sampling Methods, Kaizar – p.1/12 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 Linear Regression in a Nutshell Assume the following model: Y i | x i = β + β 1 x i + ǫ i E ( ǫ i ) = 0 V ( ǫ i ) = σ 2 Cov ( ǫ i ,ǫ j ) = 0 Goal: Estimate β 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 = ¯ 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- ˆ β 1 x i parenrightBig 2 / ( n- 2) ∑ ( x i- ¯ x ) 2 STAT 651: Survey Sampling Methods, Kaizar – p.5/12 Finite Population Setting...
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This note was uploaded on 07/26/2011 for the course STA 651 taught by Professor Kaizar during the Winter '11 term at Ohio State.

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

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