FOR MATHGUY18 ONLY

You will notice, however, that both SEX and RACE are nominal variables, not I/R variables. Since we told you that regression is appropriate for I/R continuous variables, you may begin to wonder how we can propose to use two nominal variables in a regression equation. That’s a very good question.

The answer lies in the fact that researchers sometimes treat such items as  dummy variables  to make them appropriate for a regression analysis. In regard to the variable SEX, for example, one can transform gender into a measure of “maleness,” with male respondents being 100% male and female respondents being 0% male.

Recoding SEX to Create a Dummy Variable: MALE

Let’s recode SEX as described above into the new variable MALE. So take the following steps:

· Transform → Recode → Into Different Variables

Select SEX as the numeric variable. Let’s call the new variable MALE. Using the Old and New Values window, make these assignments.

Execute the Recode command by clicking Continue and then OK.

Before moving on to the variable RACE, make sure you set the decimal places for MALE to 0. You may also want to give a brief description of MALE and define your values and labels (e.g., “male” and “not male”). It might be a good idea to check the Data View window and verify that your coding is accurate: Cases with a 1 for SEX should also have a 1 for MALE, while cases with a 2 for SEX should have a 0 for MALE.

Recoding RACE to Create a Dummy Variable: WHITE

We will use the same basic procedure to recode RACE as we used to recode SEX. Open the Recode dialog box by selecting Transform → Recode → Into Different Variables.

Designate RACE as the numeric variable and name the new variable WHITE. Then use the Old and New Values window to accomplish your recode.

You will notice that unlike the variable SEX, RACE contains three values: 1 (“White”), 2 (“Black”), and 3 (“other”). Consequently, in this case we are going to recode RACE as follows:

With this coding scheme, the dummy code 1 designates 100% majority group status; 0 designates 0% majority group status. Once you have set the new values, click Continue and OK to execute the command.

Before we ask SPSS Statistics to run our regression analysis, make sure you set the decimal places for your new variable (WHITE) to 0. In addition, you may want to provide a brief description of the variable and define the values and labels (e.g., “white” and “not white”). Again, it wouldn’t hurt to take a look in the Data View window to verify that your coding is accurate: Cases with a 1 for RACE should also have a 1 for WHITE, and cases with a 2 or 3 for RACE should have a 0 for WHITE.

SPSS Statistics Command 17.2: Recoding to Create a Dummy Variable

Multiple Regression

Now that we have created our dummy variables, we are ready to request the multiple regression analysis.

Analyze → Regression → Linear takes us to the window we want. Select EDUC and make it the dependent variable. Then place PAEDUC, WHITE, and MALE in the “Independent(s):” field. In the “Method:” drop-down menu, the “Enter” method is probably displayed by default. If not, select it by clicking on the down arrow.

Run this command by clicking OK, and you will receive a mass of output. Without going into all the details, we are simply going to show you how it establishes the equation we asked for. We’ll take the output a piece at a time. For our purposes, we’d like you to skip through the output on your screen until you find the following tables:

We have given SPSS Statistics three variables that we felt might help predict occupational prestige.

To create our equation, we take two numbers from the “Unstandardized Coefficients” column: the constant (9.919) and the β (beta) value (called the slope) for PAEDUC (0.361), WHITE (–0.094), and MALE (–0.259). Locate those in your output. We use these numbers to create the following equation for EDUC, based on the standard regression model for the predicted value of Y:

Ŷ = a + bX1 + bX2 + bX3

EDUC = 9.919 + (PAEDUC × 0.361)* + (WHITE × –0.094) + (MALE × –0.259)

= 9.919 + (PAEDUC × 0.361)* – (WHITE × 0.094) – (MALE × 0.259)

We’ll explain the asterisk in the above equation shortly. In the meantime, how would you predict years of education of a White male whose father had 12 years of education? Here is a hint to get you started:

EDUC = 9.919 + (12 × 0.361) – (_____ × _____) – (_____ × _____) = _______

The column titled “Standardized Coefficients” gives you a guide to the relative impact of the different variables. Take a minute to consider some independent variable that has no impact on the dependent variable. What slope would it be given? If you think about it, the only proper weight would be zero. That would mean that a person’s value on that variable would never make any difference in predicting the dependent variable. By the same token, the larger the slope for any given variable, the larger its part in determining the resulting prediction.

It is possible that a variable that is supposed to be a better predictor, such as PAEDUC, could have a smaller slope than an item such as MALE, which is not supposed to be as good a predictor of EDUC. How can this happen? The solution to this puzzle lies in the different scales used in the different variables. MALE goes only as high as 1 (“male”), whereas PAEDUC obviously goes much higher to accommodate differences in the levels of education of respondents. Slopes must be standardized before they can be compared. Standardized slopes are what the slopes would be if each of the variables used the same scale.

SPSS Statistics prints standardized slopes under the column “Standardized Coefficients.” The data presented above indicate that PAEDUC (0.493) has the greatest impact on EDUC, followed distantly by WHITE (–0.012) and MALE (–0.041). Interpreted, this means that father’s education has the greatest impact on one’s own educational level, followed by “maleness” and then “racial majorityness.”

Significance levels of the coefficients also add information about the likelihood of their impact on the dependent variable. Look at the column labeled “Sig.” Here, this value can be interpreted as we have discussed earlier in this book. As a rule of thumb, anything at.05 or less is considered significant; such values are usually denoted with an asterisk in a report. The only independent variable in this equation that turned out to be statistically significant (.000) was PAEDUC, father’s educational attainment. This explains the appearance of the mysterious asterisk in the equation above!

Other variables exist within your DEMO.SAV file that you could add to the mix of independent variables for a regression analysis. One such variable that might prove particularly interesting is MAEDUC, mother’s educational attainment. How does the impact of mother’s educational attainment compare to that of PAEDUC, father’s educational attainment? Go back to the linear regression dialog box and begin that adventure!

SPSS Statistics Command 17.3: Multiple Regression

Conclusion

In this chapter, we have given you an initial peek into the logic and techniques of multivariate analysis. As you’ve seen, the difference between bivariate and multivariate analysis is much more than a matter of degree. Multivariate analysis does more than bring in additional variables: It represents a new logic for understanding social scientific relationships.

In this introduction to multivariate analysis, we’ve looked at how it lets us explore the nature of multiple causation, specifically how two or more independent variables may affect a dependent variable. In addition, we’ve used multivariate techniques to test the generalizability of relationships.

In the latter regard, we have begun using multivariate techniques for the purpose of considering hidden relationships among variables, as when we asked whether the widowed attended church frequently not because of their marital status but because they were mostly older people. We’ll pursue this kind of detective work further in the chapters to come.

Main Points

· ■ This chapter introduced a new, more sophisticated form of statistical analysis: multivariate analysis.

· ■ Multivariate analysis is the simultaneous analysis of three or more variables.

· ■ The crosstabs procedure can be used to analyze the relationship between an independent variable and a dependent variable while controlling for a third variable.

· ■ We examined multiple causes of religiosity in more depth by focusing on items such as AGECAT, SEX, MARITAL, and CLASS.

· ■ Other analytic techniques that may aid in the examination of several items at once include chi-square, measures of association, and regression.