Page 354 - Applied Statistics with R

354 CHAPTER 14. TRANSFORMATIONS

## Model 1: y ~ poly(x, 2)
## Model 2: y ~ poly(x, 4)
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 247 2334.1
## 2 245 1912.6 2 421.51 26.997 2.536e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

fit_6 = lm(y ~ poly(x, 6), data = data_higher)

anova(fit_4, fit_6)

## Analysis of Variance Table
##
## Model 1: y ~ poly(x, 4)
## Model 2: y ~ poly(x, 6)
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 245 1912.6
## 2 243 1904.4 2 8.1889 0.5224 0.5937

14.2.5 poly() Function and Orthogonal Polynomials

4
3
2
= + + + + +
0
2
1
4

3
fit_4a = lm(y ~ poly(x, degree = 4), data = data_higher)
fit_4b = lm(y ~ poly(x, degree = 4, raw = TRUE), data = data_higher)
fit_4c = lm(y ~ x + I(x^2) + I(x^3) + I(x^4), data = data_higher)
coef(fit_4a)
## (Intercept) poly(x, degree = 4)1 poly(x, degree = 4)2
## -1.980036 -2.053929 -49.344752
## poly(x, degree = 4)3 poly(x, degree = 4)4
## 0.669874 20.519759

coef(fit_4b)

## (Intercept) poly(x, degree = 4, raw = TRUE)1
## 2.9996256 -0.3880250
## poly(x, degree = 4, raw = TRUE)2 poly(x, degree = 4, raw = TRUE)3
## -6.1511166 0.1269046
## poly(x, degree = 4, raw = TRUE)4
## 1.0282139