The logistic regression model is one of the oldest and most common of the regression models, and it is known as one of the statistical methods used to describe and estimate the relationship between a dependent random variable and explanatory random variables. Several methods are used to estimate this model, including the bootstrap method, which is one of the estimation methods that depend on the principle of sampling with return, and is represented by a sample reshaping that includes (n) of the elements drawn by randomly returning from (N) from the original data, It is a computational method used to determine the measure of accuracy to estimate the statistics, and for this reason, this method was used to find more accurate estimates. The maximum potential and the character regression estimations were found in estimating the two-response logistic regression model by adopting the bootstrap method and comparing the estimations according to the standard mean squares of error (MSE).It was evident through comparison that the character regression method in estimating the two-response logistic regression model by adopting the bootstrap method is the best in estimating the logistic regression model parameters as it has less (MSE).