TABLE VI-4. Summary of statistical values calculated
 for the linear and the quadratic equations.

Statistic Linear Quadratic
R2 0.813 0.920

Sy.2 or Sy.122 0.152 0.0868

tb 4.1616** ---

tb 3.4590**

tb2 2.0160*

Fc (equation) 17.38** 17.21**

Fc (quadratic -4.0058 N.S.
 term)

**Significant at a 5% level
* Significant at a 10% level

 On the basis of pure statistical analysis, the
quadratic surface might be rejected in favor of the linear
surface even though the R2 is better for the quadratic
surface. The rejection of the quadratic surface would be
based on the t test of the coefficient b2 and of the F
test of the same term. The t test indicates that the
coefficient b2 is significantly different from zero only
at the 10% level, and the F test indicates that including
the quadratic term does not improve the estimate of the
response.
 Theory and experience with surfaces, and in
particular, response to nitrogen, assure us that over a
wide range of application, response should not be linear.
In this case, the range of application of nitrogen appears
to be adequate to give a curvilinear response, and it does
appear that the mean values of the observations fall on a
curve, not on a straight line. On the other hand, it is
possible that experimental results indicate a curve that
is more complex than a quadratic curve. That is, within
the range of application in the experiment it is possible
that all three stages of production exist. However, with
only three treatment levels in this experiment it is not