Remarkably, given a collection of points, it's possible to find a relatively small polynomial which passes through those points exactly. This polynomial model is pretty simple and a really good fit for our data (a perfect fit for our data!), which might lead us to believe that it's a good model, potentially useful for making predictions. In this interactive, we'll see that it is not.
Pick a number of data points (n) and enter some data below. If you like, you can click on one of the buttons below to load a prefetched data set.
Below, I'll walk you through the steps to figure out the lagrange polynomial fitting the data points entered above. It's suggested that you enter a really simple data set with at least three non-colinear integer points such as (0,1),(1,2),(2,4) .