Optimal Design Of Three Variables Random Coefficient Regression Model Under Different Variance

Optimal design is an important branch and hot spot in the research of experimental design. This paper studies mainly D- optimal design problem of the three variables random coefficient regression model under different variance on the unit cube.Loewner as a tool reduces dimensionality of solving optimal design problem. And the random intercept, slope and random error are uncorrelated, random error is the difference.It is proved that when the variance function of the random error satisfies certain condition, the D- optimal design can be found in the design category of the design domain vertex.Calculate the numerical results of the D- optimal design and the D- efficiency of the three variables random coefficient regression model by MATLAB.