Exampleof a second-degreeequationrepresentinga rising ridge.

ˆ y

=82.71

+8.80x1

+8.19x2

-6.95x1

2

-2.07x2

2

-7.59x1x2

ˆ y

-87.69

=

- 9.02X
1

2

+2.97X2

were true that bias could be ignored so that the postulatedmodel function were capab
xactly representing reality, then atx = (x1,x2, . . . . xk)'

E(yx) =ηx

the standardized mean squared error associated with estimatingit byˆ
y
x

Vx=n?
σ2

would be

?

?

?
? ? Vˆ y

x

ereVxwill be called thevariancefunction.
rmation functionof the designdefinedby

Equivalently, we may consider the

Ix

=Vx

-1

r example, for the factorial design illustrationinthe foregoing section,

Ix

=

4

(1

+x1

2

+x2
2)

Information surface for a 22factorial used as a first-order design.

The corresponding information contours.