# 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)``````