Business Experiments with R. B. D. McCullough
to give credit to people who are likely to default, and if we do give credit, we don't want to give more than the person can repay.
Table 1.1 Credit default rates for men and women.
| Female | Male | |
|---|---|---|
| 0 | 14 349 (79%) | 9 015 (76%) |
| 1 | 3 763 (21%) | 2 873 (24%) |
| Total | 18 112 | 11 888 |
A simple crosstab in Table 1.1 with the data shows that men are more likely to default than women. Another crosstab in Table 1.2 shows that divorced/widowed (other) persons are more likely to default.
Table 1.2 Credit default rates by marital status.
| Married | Single | Other | |
|---|---|---|---|
| 0 | 10 453 (77%) | 12 623 (79%) | 288 (76%) |
| 1 | 3 206 (23%) | 3 341 (21%) | 89 (24%) |
| Total | 13 659 | 15 964 | 377 |
Try it!
We encourage you to replicate the analysis in this chapter using the data in the file credit.csv . Computing crosstabs can be done in a spreadsheet using pivot tables. Most statistical tools also have a cross‐tabulation function.
df <- read.csv("credit.csv",header=TRUE) # Table 1.1 table1 <- table(df$default,df$sex) # to get the counts table1 # to print out the table prop.table(table1,2) # to get column proportions prop.table(table1,1) # to get row proportions
In addition to the categorical variables in our data set like sex and marital status, we also have continuous variables like age. Perusing the boxplots in Figure 1.2, it appears that persons who do not default have higher credit limits than persons who default, while age appears to have no association with default status.
Figure 1.2 Boxplot of default vs. non‐default for credit limit and ages.
If it is really the case that persons with higher credit limits are less likely to default, can we decrease the default rate simply by giving everybody a higher credit limit?
Software Details
To reproduce Figure 1.2, load the data file credit.csv …
boxplot(limit∼default, xlab="default", ylab="credit limit", data=df)
We have thus far looked at how the four variables are associated with default, individually. How might we examine the effects of all the variables at one time in order to answer the two fundamental questions?
The answer, of course, is to use regression to relate default to all four variables at once. Since default is a categorical variable with two levels, linear regression is not appropriate. We would have to use logistic regression instead. As for the independent variables, credit limit and age are continuous and require no special treatment before being included in the regression (though it may be advantageous to turn each into a categorical variables with, say, categories “low,” “medium,” and “high”). Sex and marital status are categorical variables and will have to be included as dummy variables. If you are unfamiliar with the creation of dummy variables, sex can be represented by a single dummy variable, say,
Marital status (married, single, or divorced/widowed) will be represented by two dummy variables,
For a married person,
1.2.1 Lurking Variables
It is not uncommon for an analyst to reach mistaken conclusions based on observational data that are incorrect due to lurking variables.
1 During WWII, an analysis of the accuracy of strategic bombing runs showed that Allied bombers were more accurate at lower altitudes than at higher altitudes (this makes sense). The analysis also showed that Allied bombers were more accurate when opposed by enemy fighters than when enemy fighters were not present. Explain.
2 A scatterplot shows a strong relationship between the number of firefighters at a fire and the dollar amount of the damage caused by the fire. While this relationship may be predictive, it is not causal: it is not true that if fewer firefighters are sent to a fire, the dollar amount of the damage will decrease. What is the missing causal variable?
3 On a daily basis in a coastal town, there is a positive relationship between ice cream sales and drowning deaths. What is the missing causal variable?
4 The observational data repeatedly say that persons who eat five fruits and veggies per day have a lower cancer rate than those who don't eat fruits and veggies. The experimental results find no difference in cancer rates. Explain the discrepancy.
5 A large, expensive observational study by the National Institutes of Health concluded that hormone replacement therapy (HRT) prevents heart disease in postmenopausal women. Consequently many women were placed on HRT. Later, an experiment showed that HRT does not prevent heart disease in postmenopausal women. Explain the discrepancy.
The resolutions of the above