Regression

Bivariate Regression

Social scientists often want to examine the relationship between two variables. To illustrate, an empirical example is unfolded. Imagine that educational sociologists in a small midwestern college seek information on the annual earnings of their students well after graduation. They want to know many things, including the influence of basic demographic forces, such as the socioeconomic background of the students’ families. In particular, they seek to establish the link, if any, between the educational attainment of parents and the later job earnings of the child. To gather the necessary data on these and other research questions, they draw a RANDOM SAMPLE from the alumni list of 350 students who graduated 15 years ago. Because of cost considerations, they sample 1 out of 10, yielding a sample size of 35. Table 1 contains some of the data from the survey administered to them. In column 1 is the code number given the student. In column 2 is the parent education variable, measured as the number of years of formal schooling completed by the most educated parent (mother or father). In column 3 is the student income variable, measured as the reported gross annual income (in thousands of dollars) the student earned 15 years after graduation. In column 4 is the gender of the student, scored 1 = male or 0 = female. These data are listed as they would appear when entered into a typical computer STATISTICAL PACKAGE.

The research question at hand is whether parent education (variable X1) helps account for later student income (variable Y). The dominant HYPOTHESIS is that they are positively related. The more educated the parental environment, the more child opportunities and incentives for learning and advancement and, ultimately, higher income on the job. Does an analysis of the data support the hypothesis? In bivariate regression, the first step is inspection of a SCATTERPLOT, asin Figure 1.

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