Suppose that you have fit the following model

̂y = 20 + 10x1 − 4x2 + 12x3

(a) The experimenter decides to choose x1 as the variable to define the step size for steepest ascent. Do you think that this is a good choice for defining step size? Explain why or why not.

(b) The experimenter decides to make the step size exactly one coded unit in the x1 direction. Find the coordinates of this point from the design center on the path of steepest ascent.

(c) Suppose that you had used x3 as the variable to define the direction of steepest ascent. Assuming a step size of one coded unit, find the coordinates of the first step in this direction away from the design center.

(d) Find the distance between the two points found in parts

(b) and (c), respectively.