A short cut method for linear regression

This thesis reviews and discusses the so-called “Group Averages method" in the linear regression, the quadratic regression, and the functional relation situations.

In the linear and quadratic regression situations, under the assumption of X_i equally spaced, the efficiency of the Group Averages estimator is quite satisfactory as compared with Least Squares estimators.

In the functional relation situation we used the Group Averages method and the Maximum Likelihood method for estimation of parameters. To compare their efficiencies we used the variance of the Group Averages estimator which was given by Dorff and Gurland [3], and developed the variance of Maximum Likelihood estimators. Under the assumption of X_i equally spaced, we round the efficiency of the Group Averages estimator to be quite satisfactory. However, caution is needed for using the Group Averages method in functional relationships, since it requires the following condition to be satisfied:

Pr {|d_i| ≥ ½ c} negligible Where c = Min. |X_i+1 - X_i|.