关于饱和D—最优设计的再商榷

以试验误差理论为基础，通过误差类型和自由度的划分，论证回归设计的实质是通过增大信息矩阵A的行列式来减少模型误差，提高回归方程的拟合性，而与试验随机误差无关; 至于能否对回归方程进行拟合性检验，则取决于是否有剩余自由度。饱和D—最优设计A的行列式最大，在给定回归模式和设置重复的条件下所需的试验处理数也最少，因而是最优设计。本文还结合肥料田间试验特点，对现代回归设计的农业应用进行了讨论。

Reconsideration of saturated D-optimal design

Based on experimental error theory, the objective of regression design is to improve fitness of equation through enlarging the determination of error type information matrix A and thus reduce model error on basis of classification of error types and degree of freedom, which is independent of random error. Whether the significant difference of regression equation in fitness can be tested is dependent on residual degree of freedom. Saturated D-optimal design has the maximum determinant of information matrix A. Under the given regression model and number of replication, there was a minimum number of treatments in the experiment of Saturated D-optimal design which is characterized of optimization. Agricultural application of modern regression design was discussed in combination with properties of fertilizer field experiment.