Bivariate Regression

Regression is a statistical technique used to help investigate how variation in one or more variables predicts or explains variation in another variable. This popular statistical technique is flexible in that it can be used to analyze experimental or nonexperimental data with multiple categorical and continuous independent variables. If only one variable is used to predict or explain the variation in another variable, the technique is referred to as bivariate regression. When more than one variable is used to predict or explain variation in another variable, the technique is referred to as multiple regression. Bivariate regression is the focus of this entry.

Various terms are used to describe the independent variable in regression, namely, predictor variable, explanatory variable, or presumed cause. The dependent variable is often referred to as an outcome variable, criterion variable, or presumed effect. The choice of independent variable term will likely depend on the preference of the researcher or the purpose of the research. Bivariate regression may be used solely for predictive purposes. For example, do scores on a college entrance exam predict college grade point average? Or it may be used for explanation. Do differences in IQ scores explain differences in achievement scores? It is often the case that although the term predictor is used by researchers, the purpose of the research is, in fact, explanatory.

Suppose a researcher is interested in how well reading in first grade predicts or explains fifth-grade science achievement scores. The researcher hypothesizes that those who read well in first grade will also have high science achievement in fifth grade. An example bivariate regression will be performed to test this hypothesis. The data used in this example are a random sample of students (10%) with first-grade reading and fifth-grade [Page 87]science scores and are taken from the Early Childhood Longitudinal Study public database. Variation in reading scores will be used to explain variation in science achievement scores, so first-grade reading achievement is the explanatory variable and fifth-grade science achievement is the outcome variable. Before the analysis is conducted, however, it should be noted that bivariate regression is rarely used in published research. For example, intelligence is likely an important common cause of both reading and science achievement. If a researcher was interested in explaining fifth-grade science achievement, then potential important common causes, such as intelligence, would need to be included in the research.