Optimal Design Of Relevant Regression Model

Single response linear regression model has been studied in many literat ures, the optimal design problem of single regression model is also very mature, H.Dette(2011) gives the optimal design of single response linear regress ion model with relevant observations. due to the change of dimensions, the complexity of the relationship between the random error, the optimal design of multi-response linear regression model with relevant observations will become more complex.In this article, we consider optimal design for multi-response linear regression model with related observations. We mainly discussion of two-response linear regression model. When the random error is associated, we focus on optimal design for two-response linear regression models with observations related. In this paper, Firstly, we get the least squares estimation of unkno wn parameters.Then, we can get the covariance matrix of the estimator. Secondly, we build new optimal criteria which based on the optimal criteria of single-response model. We call the optimal criteria is g-optimal criteria, At last we give the necessary condition to achieve the g-optimal criteria. As the function in g-optimal criteria is very complex, it is difficult to obtain accurate analytical solution, so we give the numerical analysis algorithm to obtain g-optimal criteria.