note10 - STAT5044: Regression and Anova Inyoung Kim Outline...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
STAT5044: Regression and Anova Inyoung Kim
Background image of page 1

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

View Full DocumentRight Arrow Icon
Outline 1 Polynomial Regression
Background image of page 2
Polynomial Regression (nonlinearity) Using taylor series approximate polynomial function m th order polynomial, y i = β 0 + β 1 x i + β 2 x 2 i + ··· + β m x m i + ε i , ε i N ( 0 , σ 2 ) . The number of parameter p = m + 1 y = 1 x 1 x 2 1 ··· x m 1 1 x 2 x 2 2 ··· x m 2 . . . . . . . . . ··· . . . 1 x n x 2 n ··· x m n β 0 . . . β m + ε = X [ m ] β + ε Polynomial regression is still a linear model (linear model of parameter)
Background image of page 3

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

View Full DocumentRight Arrow Icon
General Anova H 0 : there is no “polynomial type of relationship” between x and y . ⇐⇒ β 1 = β 2 = ... = β m = 0 H 1 : at least one β i ( i 1 ) does not equal to zero. Full model (general model) Y i = β 0 + β 1 x i + β 2 x 2 i + ... + β m x m i + ε i Reduced model (corespond to H 0 ) Y i = β 0 + ε i
Background image of page 4
General Anova Residual sum of square RSS ( β 0 , β 1 ,..., β m ) = n i = 1 ( y i - ˆ β 0 - ˆ β 1 x i -···- ˆ β m x m i ) 2 RSS ( β 0 ) = n
Background image of page 5

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

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/02/2012 for the course STAT 5044` taught by Professor Staff during the Fall '11 term at Virginia Tech.

Page1 / 15

note10 - STAT5044: Regression and Anova Inyoung Kim Outline...

This preview shows document pages 1 - 6. Sign up to view the full document.

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