Confused about polynomial regression with multiple variables

Question

I'm trying to create a multivariable polynomial regression model from scratch but I'm getting kind of confused by how to structure it.

So, I have an array of feature vectors such that each vector can be displayed like so:

[height, weight, age]

I know with multivariable linear regression I would create an algorithm like so:

y=B₀+B₁*x₀+...B_n*x_n

Where x₀ would be the first element of each in the feature vector.

So for multiple variable polynomial regression would it go something like this:

y = B₀+B₁*x₀+B₂*x₁**2+...B_n*X_n**d

Where d is the degree of the polynomial. Apologies if this is painstakingly obvious and formatted badly, I'm just a small bit lost.

Answer 1

Not exactly,
Polynomial regression means that the dataset is not linear and we have to transform it to a specific polynomial degree based on the dataset, so that we may map the Linear model

Decide a polynomial degree first, let's say 2
$y=b_0+b_1*x_0^2+b_2*x_1^2+...b_n*x_n^2$

If we want to add feature interaction,
$y=b_0+b_1*x_0^2+b_2*x_1^2+b_3*x_0*x_1....$

Basically, you have to implement this Class of Scikit-Learn
PolynomialFeatures