1.  Choosing a Topic

1. Use your own dependent variable and a data set that you already have or that you can easily obtain.  Using your own data set and model is highly encouraged as long as
 
1. you have a dependent variable that is at least arguable continuous (this might be an ordinal variable with, say, 4 categories)
2. you follow the outline of analysis below (although your data set may have different kinds of issues than the ones illustrated below and your analysis should differ accordingly)
3. you do not spend a lot of time collecting the data and agonizing about substantive issues (since the focus of this paper is on the mechanics of regression analysis, not the substantive issues)
2. Do the analysis of income inequality using the world209 data set as outlined below
3. Choose and analyze another dependent variable from the world209 data set
4. Channel Blau and Duncan by using one year of the GSS data to do an analysis of the determinants of occupational prestige (PRESTIGE) on years of education (EDUC), father's occupation (PAPRES16), father's education (PAEDUC), cognitive ability (WORDSUM), SEX and other variables you may think of.  Compar the achievement model for men and women, or for blacks and whites.  You can see the beginning of such an analysis on my Social Stratification site at http://www.unc.edu/~nielsen/soci230/odocs/status.htm
5. If you are interested in real estate do a regression analysis of the data set for home prices in a mid-western town, from the point of view of a real estate consultant trying to discover the most important attributes of a house in determining sale price
6. Use a dependent variable of your choice with any (sufficiently rich) data set that may be available through the course site or on the CD that comes with the textbook, with the same proviso about following the general outline of analysis below

2.  Outline for Analysis of Income Inequality in World Handbook Data

z:\asnt1\users\sociology\students\bardot

Part 1 - Do the Analysis

SYSTAT commands (you can replace myresid with a more imaginative file name):
mglh
model v152=constant+v286
save
save myresid
estimate

SYSTAT commands:
stats
box residual
stem residual
pplot residual

5.  Run descriptive statistics and plots (box and stem and leaf) for all the variables.  Any outliers?  Create a correlation matrix of all of your variables and a splom (or let SYSTAT produce the splom automatically when you produce the correlations).  Look at the relationships between the dependent variable v152 and all the potential independent variables in the splom.  Are these relationships linear?  If you suspect nonlinearity, redo the splom specifying smooth=lowess to see if a curvilinear relationship appears.  If you find (a) curvilinear relationship(s), think of the possibility of transforming the variable(s) or using polynomial regression to model the curvilinearity.

6.  At this point if I (Nielsen) ask myself "how would I do it" I realize that what I would actually do is estimate first the full model, with all the independent variables I have selected, and do a comprehensive analysis of potential problems with that regression (outliers, collinearity, heteroskedasticity, etc.).  I would decide how to deal with eventual outliers and influential cases at this stage too.  Then, when the data set is "cleaned up" (for instance, if I have decided to exclude deviant observations) I would redo all the regressions starting with the first model, and introducing additional variables in turn.  I would not redo the whole diagnostic shebang for each one of the intermediate regression models.

7.  Estimate several multiple regression models in which you successively add the additional independent variables, singly or in groups of substantively related variables (such as a polynomial function consisting of an independent variable and its square, or a set of indicators representing the same categorical variable, or variables pertaining to the same substantive area, such as "labor force composition" variables).  [Save the residuals of each regression - but see 6.]  Note (for yourself) the following:  What does the R² indicate about the fit of the model?  Is the overall model significant?  Are individual coefficients statistically significant, and if so at what level?  Interpret the regression coefficient for each additional independent variable.  Is the relationship positive or negative?  What does the coefficient mean in terms of the effect of the variable on income inequality?

8.  In any of the models, is there evidence of collinearity?  How can you tell?  If so, find a way to deal with it.

9.  [But see 6.  You can do the whole treatment only for the full model.  And estimate the intermediate models afterwards.]  For each model look at the scatter plot of the residuals against the estimate that SYSTAT produces automatically with the regression.  Produce a box plot, stem and leaf, and normal probability plot of the residuals.  Look at the diagnostics for outliers and influential cases.  What do they indicate?  Do you find evidence of other problems (such as heteroskedasticity, outliers and/or influential cases, nonlinear relationships)?  How can you tell?  If so, decide whether you need to take corrective action.

Part 2 - Write-Up the Results

Prepare your results in standard publication style tables.  You will need to prepare two tables.

• Table 1 contains the correlation matrix of all the variables, with the basic statistics for all variables (mean, standard deviation, minimum value, maximum value).  The basic statistics are often combined with the correlations as the last row of the correlation matrix.  See the following published examples for models (I prefer the second example because it has the minimum and maximum values of the variables).

Exhibit: model for Table 1 (from Firebaugh, Glenn.  1983.  ASR 48:263.)

Exhibit: another model for Table 1 (from Nielsen, François.  1994.  ASR 59:668)
 

• Table 2 contains the regression results.  The leftmost column is the regression of v152 on v286.  Successive columns show the regressions of v152 on v286 and additional variables that you add singly or in groups (if the group make sense substantively).  The last column contains the most inclusive model, or a trimmed model if you decide to drop variables that are non significant in the most inclusive model (in which case, you know what test you need to carry out, right?).

Write the paper using the following sections.

1.  Introduction - Explain the dependent variable and the independent variable, and what relationship you expect to find between the proportion of the labor force in agriculture and income inequality.  Then list the other independent variables you have selected and explain why you have selected them, and how you expect these variables to be related to income inequality and/or how you expect the inclusion of these variables to affect the original relationship between income inequality and labor force in agriculture.  (This may be very short.  In a real paper this is where you would place a review of the literature, summarize relevant debates in the field, etc.).

2.  Data - Explain how the variables are measured, including the units (from the variable lists).  Insert Table 1 in this section and refer to Table 1 to discuss any unusual feature of the data, such as very high correlations between independent variables.  If you have had to transform one or several variables, explain what transformation(s) you have used and why (e.g., to model a nonlinear relationship, etc.).  This section too may be very short -- if you haven't done anything too perverse with your data.

3.  Methods - Explain that you will be using multiple regression analysis and what auxiliary analyses you have performed.  List the diagnostic tests you have carried out, and any corrective action that you have taken.  For example, if you have thrown out some influential cases, explain who they are and why you have dealt with them that way.  (If you have had to use the Zarathustra-KR2 algorithm and the Buzz-Lightyear correction to treat an extremely exotic pathology in your data, this is where you explain that too.)

4.  Results -  Discuss the columns of Table 2 in turn.  For each model, describe the effect(s) of the newly introduced variable(s), their significance, direction, and how introducing the new variables does or does not affect the coefficients of variables that are already in the model.  Finally discuss the most inclusive model, or the trimmed model if you estimated one (in which case report the result of the test of joint significance for the variables you dropped).

5.  Conclusion - Summarize the major highlights of your analysis of income inequality.  What further research should be done to extend your results (i.e., what variables that is not available in the file would you like to add to the model, what additional data should be collected)?

Turn in any relevant additional output as an appendix only if you think it is relevant.  This may include graphs or auxiliary analyses that document a particular problem with the data.  You do not need to provide copies of all the analyses you carried out.