Codes anova test analysis deviance table model gamma

INFT13/71-326
Statistical Learning and Regression Models Indicative Solutions
Week 10

Load some of the usual suspects:

8	10	14		65	70	75	80
8	10			65	trees$Height

# Start with linear regression, but maybe some heteroskedasticity, so might need to switch to # Gamma model.

10	20	30	40	50	60	70

fitted(trees.lm)

fitted(trees.glm)

fitted(trees.lm)

u1 <- trees$Volume - cbind(1,trees$Height)*%%coef(trees.lm)[c(1,3)] u2 <- trees$Volume - cbind(1,trees$Girth)%%coef(trees.lm)[c(1,2)] plot*(trees$Girth,u1,pch=16)

plot(trees$Height,u2,pch=16)

trees$Height

trees$Girth

plot(trees$Girth,v1,pch=16) abline(coef(lm(v1~trees$Girth)),lty=3,col=2)

#So, let's see if a quadratic term in Girth is significant trees.lmq <- lm(Volume~Height+Girth+I(Girth^2),data=trees) trees.glmq <- glm(Volume~Height+Girth+I(Girth^2),family=Gamma(link="identity"),data=trees) anova(trees.lmq)
## Analysis of Variance Table ## ## Response: Volume

	1 2901.2		2901.2 421.113 < 2.2e-16 ***
## Girth ## I(Girth^2)
	27	186.0	6.9
## Signif. codes:

## Df Deviance Resid. Df Resid. Dev F Pr(>F)

## NULL 30 8.3172

## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#Clearly, quadratic term is significant. Try height^2? Maybe girth^3? trees.lmq2 <- lm(Volume~Height+Girth+I(Girth^2)+I(Height^2),data=trees)

	Df Sum Sq Mean Sq			F value
## Height ## Girth	1 2901.2 1 4783.0
			235.9 0.1	33.0009 4.769e-06 *** 0.0208 0.8865
	26	185.9

## Signif. codes:

trees.glmq2 <- glm(Volume~Height+Girth+I(Girth^2)+I(Height^2),family=Gamma(link="identity"),data=trees)

trees.lmq3 <- lm(Volume~Height+Girth+I(Girth^2)+I(Girth^3),data=trees) anova(trees.lmq3)
## Analysis of Variance Table ## ## Response: Volume
	Df Sum Sq Mean Sq
	1 2901.2		2901.2 408.2570 < 2.2e-16 ***
## Girth	1 4783.0
## I(Girth^2)	1	235.9	235.9

fitted(trees.lm1)

trees.glm1$linear.predictors

## [1] 155.5867

trees.glm1$linear.predictors

barplot(CooksD) abline(h=4/31,lty=3)