Stats Solutions

(Solved) A second-order response surface model in two variables

Question: A second-order response surface model in two variables is

\[\begin{aligned} \hat{y}=& 69.0+1.6 x_{1}+1.1 x_{2}-1 x_{1}^{2} \\ &-1.2 x_{2}^{2}+0.3 x_{1} x_{2} \end{aligned}\]
  1. Generate a two-dimensional contour plot for this model over the region \(-2 \leq x_{i} \leq+2, i=1,2\), and select the values of \(x_{1}\) and \(x_{2}\) that maximize \(\hat{y}\).
  2. Find the two equations given by
\[\frac{\partial \hat{y}}{\partial x_{1}}=0 \text { and } \frac{\partial \hat{y}}{\partial x_{2}}=0\]

Show that the solution to these equations for the optimum conditions \(x_{1}\) and \(x_{2}\) are the same as those found graphically in part (a).

Price: $2.99
Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document


∴ Other downloads you may be interested in ∴

log in to your account

Forgot password?
Don't have a membership account?
REGISTER

reset password

Back to
log in

sign up

Back to
log in