Lec09.PolyReg - Polynomial Regression Kutner, Nachtsheim,...

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Unformatted text preview: Polynomial Regression Kutner, Nachtsheim, Neter and Li Chapter 8.1 i i i i i i i i i i i i x x x x y x x x x y + + + + + = + + + + + = 4 4 3 3 2 2 1 4 4 3 3 2 2 1 1 Polynomial Regression Multiple Linear Regression Polynomial Regression Alligator Weight vs. Length alligator$Length 60 80 100 120 140 100 200 300 400 500 600 alligator$Weight alligator$Length 60 80 100 120 140 100 200 300 400 500 600 alligator$Weight th , 1 st , 2 nd , 3 rd Order Polynomials alligator3.lm = lm(Weight ~ Length + I(Length^2) + I(Length^3), data = alligator) summary(alligator3.lm) Coefficients: Value Std. Error t value Pr(>|t|) (Intercept) -288.3150 163.9858 -1.7582 0.0940 Length 11.8242 5.3387 2.2148 0.0385 I(Length^2) -0.1579 0.0559 -2.8247 0.0105 I(Length^3) 0.0008 0.0002 4.3870 0.0003 Third Order Polynomial alligator$Length 60 80 100 120 140 100 200 300 400 500 600 alligator$Weight th , 1 st , 2 nd , 3 rd , 4 th Order Polynomials alligator4.lm = lm(Weight ~ I(Length) + I(Length^2) + I(Length^3) + I(Length^4), data = alligator) summary(alligator4.lm) Coefficients: Value Std. Error t value Pr(>| t|) (Intercept) 327.2456 724.9689 0.4514 0.6568 Length -14.9769 31.2023 -0.4800 0.6367 I(Length^2) 0.2655 0.4887 0.5432 0.5933 I(Length^3) -0.0021 0.0033 -0.6226 0.5409 Fourth Order Polynomial Analysis of Variance 1- n ) ( Total p- n ) ( Error 1 1- p ) ( Regression Test Square Mean df squares of Sum Source 2 2 2 - = =- =- =- =- = Y Y SSTO MSE MSR Fstat p n SSE MSE Y Y SSE p SSR MSR Y Y SSR i i i i F-test Proposed Proposed Proposed Prior Proposed Prior df SS df df SS SS F-- = anova(alligator3.lm,alligator2.lm,test="F")anova(alligator3....
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This note was uploaded on 04/17/2010 for the course STSCI 3200 taught by Professor Sullivan during the Spring '10 term at Cornell University (Engineering School).

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Lec09.PolyReg - Polynomial Regression Kutner, Nachtsheim,...

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