Consider a 2nd-order response surface model that contains the linear, pure quadratic and cross product terms as follows:

y_i = β₀ + β₁x_1i + β₂x_2i + β₁₁x² _1i + Î²₂₂x² _2i + β₁₂x_1ix_2i + ϵ_i.

Fit the model above to the following data, and suggest any model editing that may be needed.

x2 -1 -1 35.38 38.42 42.15 -1 -1 36.52 45.27 53.22 37.18 -1 48.25 55.07