Now we have a form that

`lm`

can work with. We just need to specify a set of inputs that are powers of`x`

(as in a traditional polynomial fit), and a set of inputs that are`y`

times powers of`x`

. This may seem like a strange thing to do, because we are making a model where we would need to know the value of`y`

in order to predict`y`

. But the trick here is that we will not try to use the fitted model to predict anything; we will just take the coefficients out and rearrange them in a function. The`fit_pade`

function below takes a dataframe with`x`

and`y`

values, fits an`lm`

model, and returns a function of`x`

that uses the coefficents from the model to predict`y`

:

The lm function does more than just fit straight lines.