Answer and Step-by-step explanation:
Polynomial models are an excellent implementation for determining which input element reaction and their direction. These are also the most common models used for the scanning of designed experiments. It defines as:
Z = a0 + a1x1 + a2x2 + a11x12 + a22x22+ a12x1x2 + Є
It is a quadratic (second-order) polynomial model for two variables.
The single x terms are the main effect. The squared terms are quadratic effects. These are used to model curvature in the response surface. The product terms are used to model the interaction between explanatory variables where Є is an unobserved random error.
A polynomial term, quadratic or cubic, turns the linear regression model into a curve. Because x is squared or cubed, but the beta coefficient is a linear model.
In general, we can model the expected value of y as nth order polynomial, the general polynomial model is:
Y = B0 + B1x1 + B2x2 + B3x3 + … +
These models are all linear since the function is linear in terms of the new perimeter. Therefore least-squares analysis, polynomial regression can be addressed entirely using multiple regression
