METHODS OF OBTAINING RESPONSE SURFACES


Simple Regression--Visiographic

 If an experimental design includes only one input and
few treatments, and the researchers desire a quadratic
form of response surface, a simple and practical method is
to estimate the curve visually and graphically. This
requires only the simplest type of calculator. A design
using three levels of an input provides an exact estimate
of a quadratic curve. With more than three levels, the
method is less exact but still functional. Table VI-1
shows partial data from a fertilizer experiment on rice
conducted in Colombia.


Table VI-1.


Nitrogen effect on yield of IR-22 rice in
Corinto, Cauca, Colombia.


 Treatments Yields
 Replications
 N P205 K20 I II Average


 kg/ha

 0 40 40 5500 5200 5350
150 40 40 7000 6350 6675
300 40 40 6950 7000 6975

Source: Hildebrand, 1972

Nitrogen is the only input that varies in these data. The
yield of the individual replications and the mean of each
treatment level are shown graphically in Fig. VI-3. The
researchers desire to estimate a quadratic function of the
form

 Y = a + blX + b2X2

which represents the response of rice to nitrogen under
these conditions.