Linear Regression

In the late 1950s and early 1960s, the mathematics related to solving a set of simultaneous linear equations was introduced to the field of statistics. In 1961, Franklin A. Graybill published a definitive text on the subject, An Introduction to Linear Statistical Models, which piqued the curiosity of several scholars. A few years later in 1963, Robert A. Bottenberg and Joe H. Ward, Jr., who worked in the Aerospace Medical Division at Lackland Air Force Base in Houston, Texas, developed the linear regression technique using basic algebra and the Pearson correlation coefficient. Norman R. Draper and Harry Smith, Jr. in 1966 published one of the first books on the topic, Applied Regression Analysis. In 1967, under a funded project by the U.S. Department of Health, Education, and Welfare, W. L. Bashaw and Warren G. Findley invited several scholars to the University of Georgia for a symposium on the general linear model approach to the analysis of experimental data in educational research. The five invited speakers were: Franklin A. Graybill, Joe H. Ward, Jr., Ben J. Winer, Rolf E. Bargmann, and R. Darrell Bock. Dr. Graybill presented the theory behind statistics, Dr. Ward presented the regression models, Dr. Winer discussed the relationship between the general linear regression model and the analysis of variance, Dr. Bargmann presented applied examples which involved interaction and random effects, and Dr. Bock critiqued the concerns of the others and discussed computer programs that would compute the general linear model and analysis of variance. Since the 1960s, numerous textbooks and articles in professional journals have painstakingly demonstrated that the linear regression technique, presented by Bottenberg and Ward, is the same as the analysis of variance. In recent years, multiple regression techniques have proven to be more versatile than analysis of variance in handling nominal and ordinal data, interaction effects, and non-linear effects.