The purpose of this study is two-fold; the first aim being to show the effect of outliers on the widely used least squares regression 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" (R[superscript 2]). 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 attending 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 outlier/outliers, R[superscript 2] in M estimate is better alternatives than those having least squares. The findings are discussed in light of the recommendations presented in the literature.