# 9. harjoitukset
#################

# 9.3

# influenza <- read.table("C:\\Kurssit\\Glim\\Glim02\\Datat\\influenza.txt", header = TRUE, sep = ",")
names(influenza)
[1] "treatment" "response"  "frequency"

# (a)
flu.r <-glm(frequency ~ treatment + response,data=influenza, family=poisson)
flu.f <- glm(frequency ~ treatment*response,data=influenza, family=poisson)
anova(flu.r,flu.f,test="Chisq")

flu.r$deviance; flu.f$deviance; flu.r$df.residual; flu.f$df.residual

ts.r<- matrix(data = predict(flu.r,type = "response"), nrow = 2, ncol = 3, byrow = T)
ts.f<- matrix(data = predict(flu.f,type = "response"), nrow = 2, ncol = 3, byrow = T)

# Testi
pearson.res<- matrix(data = residuals(flu.r,type = "pearson"), nrow = 2, ncol = 3, byrow = T)
sum(pearson.res^2)  # Pearsonin Khin-neliötesti

# Khi^2-testisuure 17.64518, vapausasteet=2

pchisq(17.64518, 2,  lower.tail = F)
# [1] 0.0001473662
# Riippumattomuushypoteesi hylätään

# (b)
dev.res<- matrix(data = residuals(flu.r,type = "deviance"), nrow = 2, ncol = 3, byrow = T)
pearson.res<- matrix(data = residuals(flu.r,type = "pearson"), nrow = 2, ncol = 3, byrow = T)

> dev.res
          [,1]      [,2]      [,3]
[1,]  2.040115 -1.629720 -1.246900
[2,] -2.615460  1.468817  1.127679
> pearson.res
          [,1]      [,2]      [,3]
[1,]  2.206144 -1.504355 -1.153459
[2,] -2.298592  1.567394  1.201794

# Havainnot y_11 ja y_21 vaikuttavat eniten. 25 on "liian suuri" ja 6 "liian pieni",
# jotta H_0 olisi uskottava.