# Solution proposal ESL 9.6
# Based on the solutions from STK-IN4300 found here: /studier/emner/matnat/math/STK-IN4300/h24/exercises.html

library(MASS)
library(class)
library(gam)
library(rpart)
rm(list = ls())

fil= "https://hastie.su.domains/ElemStatLearn/datasets/ozone.data"

ozonedata = read.table(fil,header=T)
summary(ozonedata)
str(ozonedata) #111 observations
pairs(ozonedata)
head(ozonedata)
sum(is.na(ozonedata))

# Description
# Data frame with components: ozone, radiation, temperature, and wind.
# Measurements of daily ozone concentration (ppb), wind speed (mph),
# daily maximum temperature (degrees F), and solar radiation
# (langleys) on 111 days from May to September 1973 in New York.  This
# data frame is similar to air in SPLUS (or library(data) in S), but
# has a different definition for ozone (air contains cube-roots of
#                                       ozone).


train.set=sample(1:nrow(ozonedata),size=floor(nrow(ozonedata)*0.6),replace=F)
test.set=(1:nrow(ozonedata))[!(1:nrow(ozonedata)%in%train.set)]


#Note that gam applies 4 degrees of freedom by default
ozonedata$y<-ozonedata$ozone^(1/3)
fit.gam = gam(y~s(temperature)+s(radiation)+s(wind),data=ozonedata[train.set,],family=gaussian)
summary(fit.gam)

# plot marginal effect of radiation, for comparison with figure 6.9
# - as in figure 6.9 the ozone concentration is an increasing function for lower levels of radiation.
# - note that this plot, in contrast to 6.9, is not conditioned on the wind/temperature level.
plot(fit.gam, se = T, terms = c("s(radiation)"))

# plot marginal effects of other covariates
plot(fit.gam, se = T, terms = c("s(temperature)"))
plot(fit.gam, se = T, terms = c("s(wind)"))


# re-fit the gam-model with a spline with 3 degrees of freedom for temperature
fit.gam2 = gam(y~s(temperature,df=3)+s(radiation)+s(wind),data=ozonedata[train.set,],family=gaussian)
summary(fit.gam2)


AIC(fit.gam)
AIC(fit.gam2)
BIC(fit.gam)
BIC(fit.gam2)


# plot predicted against the true values
plot(fit.gam2$y,
     fit.gam2$fitted.values,
     xlab="y",
     ylab="y_pred",
     main="Predictions vs response",
     col="blue")
lines(c(min(fit.gam2$y),max(fit.gam2$y)),
      c(min(fit.gam2$y),max(fit.gam2$y)))
points(ozonedata[test.set,"y"],
       predict(fit.gam2,newdata = ozonedata[test.set,]),
       col="darkgreen",
       pch=7)
legend("bottomright",
       legend=c("Training","Test"),
       pch=c(1,7),
       col=c("blue","darkgreen"))




# (b) fit (a single) regression tree, PRIM and MARS
# regression tree ----
?rpart
fit.tree <- rpart(y ~ radiation+temperature+wind, data = ozonedata[train.set,], method = 'anova')
plot(fit.tree, uniform = TRUE, margin = 0.1)         # Draws the tree structure
text(fit.tree)

#