### --- SGTA Week 10 --- ###

## Question 1
turtles <- read.table("data/turtles.csv",
                      sep = ",",
                      header = TRUE)

# a
turtles_lm <- lm(eggs ~ carapace, data = turtles)
plot(turtles_lm, which = 1) # variance ok, clear nonlinearity
plot(turtles_lm, which = 2) # lots of points far away from the line, doesnt look normal

# b
turtles_quad <- lm(eggs ~ carapace + I(carapace^2), data = turtles)
turtles_cube <- lm(eggs ~ carapace + I(carapace^2) + I(carapace^3), data = turtles)

# c
anova(turtles_quad)
anova(turtles_cube)
# cubic effect is not a significant improvement to quadratic model

# d
summary(turtles_quad)
plot(turtles_quad, which = 1)
plot(turtles_quad, which = 2)
# diagnostics are better, because:
# 
#

# e
plot(eggs ~ carapace, data = turtles)
abline(turtles_lm, col = "firebrick") # THIS IS NOT THE CORRECT MODEL
x <- seq(min(turtles$carapace), max(turtles$carapace), length.out = 100)
y <- predict(turtles_quad, newdata = data.frame(carapace = x))
lines(x, y, col = "cornflowerblue")
# yhat = -899.9 + 5.871 * carap. -0.0094 * carap.^2