Specification of the Conditional Expectation by Simple Linear Regression Model For Binomial Distribution Conditioned with Varying Sample Size.

In this research, we consider the study of conditional expectation and it's relationship with regression model. The conditional expectation has a linear form which is specified as a simple linear regression model. The power transformation was used on the predictor variable which gave the best possible fit for the model which was derived from the binomial distribution conditioned with varying sampl size.The parameters of specified models were estimated by depending on emprical data which were simulated with different values for the parameter of conditional probability distribution. The best estimator for the power parameter was found in two specified models by the maximum liklihood and Draper & Smith methods. These estimators gave the best fit to the suggested model and best estimator to the conditional expectations of conditional probability distribution and it was concluded that the suggested method was better than the ordinary method.The increments in the probability of success (p) had a great effect on the best fitted model also the estimated conditional expectation of conditional binomial distribution was affected. This result was clear because of decreasing the coefficient of determination (R2) in Draper & Smith and the mean square of residuals in maximum liklihood method with increase in (p).