This example describes how to build a scatterplot with a polynomial curve drawn on top of it.

First of all, a scatterplot is built using the native R
`plot()`

function. Then, a polynomial model is fit thanks
to the `lm()`

function. It is possible to have the
estimated Y value for each step of the X axis using the
`predict()`

function, and plot it with
`line()`

.

It is a good practice to add the equation of the model with
`text()`

.

__Note:__ You can also add a confidence interval around the model
as described in
chart #45.

```
x <- runif(300, min=-10, max=10)
y <- 0.1*x^3 - 0.5 * x^2 - x + 10 + rnorm(length(x),0,8)
# plot of x and y :
plot(x,y,col=rgb(0.4,0.4,0.8,0.6),pch=16 , cex=1.3)
# Can we find a polynome that fit this function ?
model <- lm(y ~ x + I(x^2) + I(x^3))
# I can get the features of this model :
#summary(model)
#model$coefficients
#summary(model)$adj.r.squared
# For each value of x, I can get the value of y estimated by the model, and add it to the current plot !
myPredict <- predict( model )
ix <- sort(x,index.return=T)$ix
lines(x[ix], myPredict[ix], col=2, lwd=2 )
# I add the features of the model to the plot
coeff <- round(model$coefficients , 2)
text(3, -70 , paste("Model : ",coeff[1] , " + " , coeff[2] , "*x" , "+" , coeff[3] , "*x^2" , "+" , coeff[4] , "*x^3" , "\n\n" , "P-value adjusted = ",round(summary(model)$adj.r.squared,2)))
```