So I can't seem to find much on this by searching so I came here. Let's say I had 3 variables $x_1,x_2,x_3$ and the let's say the degree of the polynomial was $d=2$, I can define the length of a vector of variables as $l$ such that $l=3$ in this case. What I'm looking for is the length of a vector of coefficients that would be needed to create a polynomial regression on these variables.
Would I be right in saying that the length of the vectors of coefficients needed for polynomial regression would be $d\times l$?