I don't quite seem to understand the rules used to create the polynomial features when trying to find a polynomial model with Linear Regression in the multivariate setting.
Let's say I have a two predictor variables
b. When generating polynomial features (for example using sklearn) I get 6 features for degree 2:
y = bias + a + b + a * b + a^2 + b^2
This much I understand.
When I set the degree to 3 I get 10 features instead of my expected 8. I expected it to be this:
y = bias + a + b + a * b + a^2 + b^2 + a^3 + b^3
What is the general formula of generating multivariate features? How does this look like in the 3rd degree?