The goal of this tutorial is to learn how to do polynomial models of any degree.
library(caret)
# We are going to use the dataset mtcars
data(mtcars)
mtcars <- as.data.frame(mtcars)
str(mtcars)
## 'data.frame': 32 obs. of 11 variables:
## $ mpg : num 21 21 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 ...
## $ cyl : num 6 6 4 6 8 6 8 4 4 6 ...
## $ disp: num 160 160 108 258 360 ...
## $ hp : num 110 110 93 110 175 105 245 62 95 123 ...
## $ drat: num 3.9 3.9 3.85 3.08 3.15 2.76 3.21 3.69 3.92 3.92 ...
## $ wt : num 2.62 2.88 2.32 3.21 3.44 ...
## $ qsec: num 16.5 17 18.6 19.4 17 ...
## $ vs : num 0 0 1 1 0 1 0 1 1 1 ...
## $ am : num 1 1 1 0 0 0 0 0 0 0 ...
## $ gear: num 4 4 4 3 3 3 3 4 4 4 ...
## $ carb: num 4 4 1 1 2 1 4 2 2 4 ...
# We want to check the relationship between Milles per Gallon and Displacement
ggplot(data = mtcars) + geom_point( aes(x = mpg, y = disp)) +
xlab("Milles per Gallon (mpg)") + ylab("Distance (cu. in.)") +
ggtitle("Distance vs mpg for 1973/1974 cars") +
theme(plot.title = element_text(hjust = 0.5))
# We are going to use first a linear model
my_model1 <- lm(disp ~ mpg, data = mtcars)
# And we predict the actual data
my_pred1 <- predict(my_model1, newdata = mtcars)
ggplot(data = mtcars) + geom_point( aes(x = mpg, y = disp)) +
xlab("Milles per Gallon (mpg)") + ylab("Distance (cu. in.)") +
ggtitle("Distance vs mpg for 1973/1974 cars") +
theme(plot.title = element_text(hjust = 0.5)) +
geom_line(aes(x = mpg, y = my_pred1), colour = "red", size = 1)
# We are going to use a second degree polynomial model
my_model2 <- lm(disp ~ poly(mpg, 2), data = mtcars)
# And we predict the actual data
my_pred2 <- predict(my_model2, newdata = mtcars)
ggplot(data = mtcars) + geom_point( aes(x = mpg, y = disp)) +
xlab("Milles per Gallon (mpg)") + ylab("Distance (cu. in.)") +
ggtitle("Distance vs mpg for 1973/1974 cars") +
theme(plot.title = element_text(hjust = 0.5)) +
geom_line(aes(x = mpg, y = my_pred2), colour = "red", size = 1)
# We are going to use a 12 degree polynomial model causing overfitting
my_model3 <- lm(disp ~ poly(mpg, 12), data = mtcars)
# And we predict the actual data
my_pred3 <- predict(my_model3, newdata = mtcars)
ggplot(data = mtcars) + geom_point( aes(x = mpg, y = disp)) +
xlab("Milles per Gallon (mpg)") + ylab("Distance (cu. in.)") +
ggtitle("Distance vs mpg for 1973/1974 cars") +
theme(plot.title = element_text(hjust = 0.5)) +
geom_line(aes(x = mpg, y = my_pred3), colour = "red", size = 1)
In this tutorial we have learnt how to use polynomial models of any degree. The function poly should be used to avoid colinearity between different degrees of the same variables.