Fitting a complete second-order model. How many levels of x 1 and x 2 are required to fit the model E(y) = β 0 + β 1 x 1 + β 2 x 2 + β 3 x 1 x 2 + β 4 x 2 1 + β 5 x 2 2 ? How large a sample is...

Fitting a complete second-order model. How many levels of x₁
and x₂
are required to fit the model E(y) = β₀
+ β₁x₁
+ β₂x₂
+ β₃x₁x₂
+ β₄x²
₁
+ β₅x²
₂
? How large a sample is required to have sufficient degrees of freedom for estimating σ²?