Sosyal Bilimlerde Alternatif Regresyon Yöntemi Kullanımı ve En Küçük Kareler ile M Tahmin Yöntemlerinin Belirleyicilik Katsayısı Açısından Karşılaştırılması

Abstract

AbstractThe purpose of this study is two-fold; the first aim being to show the effect of outliers on the widely used least squares estimator in social sciences. The second aim is to compare the classical method of least squares with the robust M-estimator using the determination of coefficient (R2). For this purpose, analyzes were performed on three data sets. The first set of data is hypothetical, consisting of 15 students' general mathematic and linear algebra final scores. The second set of data was collected from 231 adolescents at- tending different high schools in Turkey. The data were collected using the Scale of Aggressiveness, Academic Self-efficacy Scale, Scale of Peer Pressure, and Trait Anxiety Inventory. The third set of data was collected from 1,385 high school students. This data were collected using the Maslach Burnout Inventory-Students Survey, Coping Styles of Stress Scale, Test Anxiety Inventory, Adolescence Self-Efficacy Scale, and Parental Attitude Scale. It was seen that, comparisons with small, medium and large volume samples, especially for the data sets including outiler/outliers, R2 in M estimate is better alternatives than those having least squares. The findings are discussed in light of the recommendations presented in the literature.Key WordsCoefficient of Determination, Least Squares, M-Estimator, Outlier, Regression Analysis, Robust Statistics.(ProQuest: ... denotes text missing in the original.)In scientific research projects, finding a relationship between two or more variables and then expressing it in a mathematical equation is an important dimension needed in order to make future predictions. This mathematical relationship does not only refer to functional relationship, but also shows that one of the variables of a predetermined value provides estimation of the other.The method that permits one to depict the relationship between variables in an equation is called regression analysis, a method which has applications in almost every field (Ariel, 1991).Regression analysis has an important role in scientific research projects because it allows a researcher to predict the future, which is one of the most important missions of science. In fact, analysis may be the most widely used statistical technique (Buyukozturk, 2005; Buyukozturk, Cokluk, K Montgomery, Peck, & Vining, 2001).It is more convenient to deal with multiple models if they are expressed in matrix notation. This allows for a very compact display of the model, data, and results. In matrix notation, the model given by Eq. (2) is:... (3)where... (4)In general, y is an n x 1 vector of the observations, X is an n x p matrix of the levels of the regressor variables, b is an p x 1 vector of the coefficients, and £ is an n x 1 vector of random errors (Montgomery et al., 2001). The major assumptions made thus far in the present study of analysis are as follows:i) The relationship between the response y and the regressors is linear, at least approximately.ii) The errors term £ has a zero mean. …