A thesis submitted to the council of the college of Administration &Economics\ University of Karbala as partial fulfillment of the requirements for the degree of Master of Statistics Sciences

By
Sara Majid Hussein Al-Kufaishi
Under supervision
Ass. Prof.  Shrook A.S.AL-Sabbah

Abstract

In order to arrive at a model that leads to accurate predictions, it is necessary to search for the method of selecting the most important variables to be included in the model, especially when the data under study suffer from the problem of Multicollinearity. And the presence of many phenomena in our daily lives, especially the social suffer from this problem, so the thesis came to compare the methods of estimating the regression parameters which it ridge regression model and the Lasso regression model. The parameters of the multiple linear models were estimated using two methods of ridge regression: the ordinary ridge regression and the method of Bayesian ridge regression, as well as the estimation of the parameters of the Lasso regression model. The comparison between the different methods is through the mean squares error MSE and the probability value P-Value. In order to apply the methods in practice, a random sample of 100 female fertility women was withdrawn to study the factors affecting the number of children born (variable response) and several independent variables (age of Wife and Husband, age of marriage, , Women’s weight, women’s use of contraception, women’s smoking, husband’s age, Wife and husband job, marriage period, number of children died, hours of exercise per week, women’s thyroid disease, hours of women’s sleep per day, take medications ,the period of breastfeeding), and the data was experiencing of Multicollinearity  problem. It was found that the Lasso regression method has the best estimation methods for possessing the least MSE, followed by the method of Bayesian ridge regression and then the ordinary ridge regression.