Abstract: The optimal design method has been widely used in the fields of engineering, and industrial and agricultural production. The study about optimal designs of random coefficient regression model is often done under the assumption that random errors are homoscedastic, but random errors are usually related to observation points and thus have heteroscedasticity. We consider the optimal approximate design of heteroscedastic random coefficient regression model on the closed intervals in this paper. Sufficient conditions are established to ensure that the optimal designs can be achieved at two extreme points of the design region. Equal-weight design on the extreme points of symmetrical design region is proved to be multiple optimal for the random coefficient regression model with symmetrical heteroscedastic errors. It doesn't depend on the heteroscedastic structure or variances of random coefficients in the model.

Key words: random coefficient regression model, heteroscedastic error, optimal design, identical design