| Abstract: | Multiple regression when regressors are measured on two different sized experimental units involves a nested error structure. This nested error structure consists of two variance components. Sufficient conditions are presented under which UMVU estimators of these variance components exist. When these conditions are not met, two alternative estimators for the two variance components are considered and compared when possible. This paper considers multiple regression models when regressor variables are associated with different sized experimental units resulting in a nested error structure. Nested error structures occur because of restrictions placed on randomizations. This results in experiments similar to splitplot type experiments which involove two different sizes of experimental units. Data resulting from these type of experiments consists of measurements made on larger sized experimental units as well as measurements made on smaller sized experimental units. Split-plot type experiments occur when certain combinations of the treatment factors are randomly assigned to larger sized experimental units after which these units are split or divided and other combinations of the treatment factors are randomly assigned to the split units. |
