1. ### --- SGTA Week 10 --- ###
2.  
3. ## Question 1
4. turtles <- read.table("data/turtles.csv",
5.                       sep = ",",
6.                       header = TRUE)
7.  
8. # a
9. turtles_lm <- lm(eggs ~ carapace, data = turtles)
10. plot(turtles_lm, which = 1) # variance ok, clear nonlinearity
11. plot(turtles_lm, which = 2) # lots of points far away from the line, doesnt look normal
12.  
13. # b
14. turtles_quad <- lm(eggs ~ carapace + I(carapace^2), data = turtles)
15. turtles_cube <- lm(eggs ~ carapace + I(carapace^2) + I(carapace^3), data = turtles)
16.  
17. # c
18. anova(turtles_quad)
19. anova(turtles_cube)
20. # cubic effect is not a significant improvement to quadratic model
21.  
22. # d
23. summary(turtles_quad)
24. plot(turtles_quad, which = 1)
25. plot(turtles_quad, which = 2)
26. # diagnostics are better, because:
27. #
28. #
29.  
30. # e
31. plot(eggs ~ carapace, data = turtles)
32. abline(turtles_lm, col = "firebrick") # THIS IS NOT THE CORRECT MODEL
33. x <- seq(min(turtles$carapace), max(turtles$carapace), length.out = 100)
34. y <- predict(turtles_quad, newdata = data.frame(carapace = x))
35. lines(x, y, col = "cornflowerblue")
36. # yhat = -899.9 + 5.871 * carap. -0.0094 * carap.^2
37.