Exercise 2 Page 219

There are different approaches we can take to decide which polynomial model would be the best choice given real-life data. We will discuss how to do this by using finite differences and by using the regression feature of a graphic calculator.

Using Finite Differences

We can determine if the real-life data fits a polynomial of specific degree by calculating the differences of the $y\text{-values}$ corresponding to equally-spaced $x\text{-values}.$ These are called finite differences. We can see an example below.