When the x1s x2s andor the xks are equally spaced the

Question

When the x₁'s, x₂'s, ... , and/or the x_k's are equally spaced, the calculation of the 's can be simplified by using the coding suggested in Exercise 15. Rework Exercise 80 coding the x₁-values -1, 0, and 1 and the x₂-values -1 and 1. (Note that for the coded x₁'s and x₂'s, call them z1's and z2's, we have not only  

Exercise 15

When the x's are equally spaced, the calculation of  and  can be simplified by coding the x's by assigning them the values ... , -3, -2, -1, 0, 1, 2, 3, ... when n is odd, or the values ... , -5, -3, -1, 1, 3, 5, ... when n is even. Show that with this coding the formulas for  and  become

Exercise 80

The following data were collected to determine the relationship between two processing variables and the hardness of a certain kind of steel:

Fit a plane by the method of least squares, and use it to estimate the average hardness of this kind of steel when the copper content is 0.14 percent and the annealing temperature is 1,100?F.