The path of steepest ascent is usually computed assuming that the model is truly first-order, that is, there is no interaction. However, even if there is interaction, steepest ascent ignoring the interaction still usually produces good results. To illustrate, suppose that we have fit the model 

ŷ= 20 + 5x₁ - 8x₂ + 3x₁x₂ 

using coded variables (-1 ≤ x_i ≤ +1).

(a) Draw the path of steepest ascent that you would obtain if the interaction were ignored.

(b) Draw the path of steepest ascent that you would obtain with the interaction included in the model. Compare this with the path found in part (a).