Week 12.
Page 225. 10,
Page 239. Exercise 6.1.
Page 248-251. Exercise 6.2, 6.3
Additional problem:
Simulation Study.
repeat 100 times.
n=8
x=rbinom(n,3,0.4)+2
t=rbinom(n,2,0.5)
x=factor(x)
y=2*x+t*t+rbinom(n,2,0.5)
u=lm(y~factor(x)+t)
summary(u)
anova(u)
y=2*x+rbinom(n,2,0.5)
u=lm(y~factor(x)+t)
summary(u)
anova(u)
y=2*x+t*t+ rnorm(n,2,0.5)
u=lm(y~factor(x)+t)
summary(u)
anova(u)
y=2*x+ rnorm(n,2,0.5)
u=lm(y~factor(x)+t)
summary(u)
anova(u)
1. In each of the above anova(u), answer the following questions:
How many hypotheses are there ? What are they ? Are they true ? Are the tests valid ?
$P(H_1|H_0)=$ ? $P(H_0|H_1)=$ ?
2. In each of the above summary(u), answer the following questions:
How many hypotheses are there ? What are they ? Are they true ? Are the tests valid ?
$P(H_1|H_0)=$ ? $P(H_0|H_1)=$ ?
3. In each of the lm(), what is the true model, the parameter $\b$, its true value,
the sample mean and SD of the LSE ?