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Towards a better Estimation of the Parameters of Linear Regression Models: The Optimal Designed Experiment Approach

 Abstract- This study investigates and compares Optimal designed Experiment with classical design which is non-Optimal using statistical tools. The two designs were evaluated on the basis of six parameters; viz, Information matrix, Dispersion matrix, Prediction variance, A-Efficiency, D-Efficiency and G-efficiency. These six parameters help to determine the better design of the two experiment. Thus, it helps to establish efficient experiment suitable for better estimation of parameters of Linear Regression Model. The result obtained in this research work showed that the D-Optimal design increased the A-Efficiency, D-Efficiency and the G-efficiency of the Initial non optimal design. Furthermore the D-Optimal design maximized the determinant of the Information Matrix, Minimized the determinant of the Dispersion matrix and minimized the trace of the Dispersion matrix. It was therefore established in this research work that the D-Optimal Design Experiment has higher statistical efficiency than the initial non-optimal design. Moreso statistical analysis of the model parameters for both designs established the D-Optimal design experiment produce better models when used for estimating the parameters of Linear Regression models. It is therefore suggested that D-Optimal approach is suitable for fixing a poorly designed experiment. It is therefore recommended for use in estimating the parameters of Linear Regression Models.