I'm new in Machine Learning and of the first concept I would like to learn is linear regression. I read that to apply linear regression I need to use a linear model. Starting from this assumption I know that this is a simple model for linear regression :
y = w0 + w1x
The definition of linear regression says that the dependent variable y should be a linear combination of the parameters w (but it is not necessary the same for the independent variable x )
So we can say that also this is a linear regression model :
y = w0 + w1x1 + w2(x2)^2
Also in this case, I should say that this is a linear regression model because for the definition, w0 , w1 and w2 are still linear in the expression. Even if there is a quadratic term for the independent variable x2.
Now , I have this question. A model like the following :
y = w1 x1 + w2 x2 + w3 x3 + w4 x1x2 + w5 (x2^3)
Is it still a linear model ? My first answer is yes , because for the definition the parameter terms are linear , but I'm not sure of it. Does anyone got any hint ?