Activity 16.4
Multiple Regression Using SPSS

Now we will do a multiple regression analysis in SPSS, trying to explain the difference in the dependent variable of income per capita in the fifty American states (perinccu) by two independent variables: (1) the level of education in the states (bachdegr), operationalized as the percentage of a state's population over 25 years old with a bachelor's degree; and (2) population density (popsqmi), measured by dividing the state's population by its area in square miles. The reasoning behind this analysis is that the income in a state is affected by these two independent variables. For the first independent variable, education, the argument is that a more educated populace will have higher-paying jobs, producing a higher level of per capita income in the state. The second independent variable is included because we expect to find better-paying jobs, and therefore more opportunity for state residents to obtain them, in urban rather than rural areas.

Open the "STATESdepr" data file in SPSS (download / help downloading). Just as you did in Activity 15.2, click on "Analyze" at the top of the screen, and choose "Regression" from the drop-down menu and then "Linear" from the next drop-down menu. A new window will appear, titled "Linear Regression." In the "Linear Regression" window, move the variable "perinccu" into the box marked "Dependent." and move both "bachdegr" and "popsqmi" into the box marked "Independent." Then click on the "OK" button. As with a simple bivariate regression, look at the "Coefficients" box to ascertain both the unstandardized and standardized regression coefficients for each of your independent variables. Look at the "Model summary" box to determine R and R².

Write a brief description about what all this tells you about the relationship among level of education, population density, and per capita income in the United States.