Write the code necessary to apply the following preprocessing steps $(2\mathrm{.}5$ points$)$:

Define a recipe with name $$diamonds$\_$recipe$3.$

Make sure that price is your dependent variable and that you use just carat, x$,$ y and z as predictors.

Scale price and carat to ensure that sd is equal to $1.$

Create an interaction term between $`$x$,$y$,$z$`.$

Keep only the last $3000$ rows.