1 Goal


The goal of this tutorial is to learn how to do polynomial models of any degree.


2 Libraries


library(caret)

3 Data import


# 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 ...

4 Plotting the dependence between variables


# 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)) 


5 Using polinomial models to predict

5.1 Linear model


# 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)