Homework 1: Example key
Rebecca Ferrell
April 6, 2016
Data description
The swiss data contain several variables pertaining to socioeconomic information of 47 French-speaking provinces of Switzerland in 1888. These include:
- Fertility: “a common standardized fertility measure”
- Agriculture: percent of males involved in agriculture as occupation
- Examination : percent of draftees receiving highest mark on army examination
- Education: percent of draftees having education beyond primary school
- Catholic: percent of the population that is Catholic (as opposed to Protestant)
- Infant Mortality: percentage of live births who live less than 1 year.
| Fertility | Agriculture | Examination | Education | Catholic | Infant.Mortality | |
|---|---|---|---|---|---|---|
| Courtelary | 80.2 | 17 | 15 | 12 | 9.96 | 22.2 |
| Delemont | 83.1 | 45.1 | 6 | 9 | 84.84 | 22.2 |
| Franches-Mnt | 92.5 | 39.7 | 5 | 5 | 93.4 | 20.2 |
| Moutier | 85.8 | 36.5 | 12 | 7 | 33.77 | 20.3 |
| Neuveville | 76.9 | 43.5 | 17 | 15 | 5.16 | 20.6 |
| Porrentruy | 76.1 | 35.3 | 9 | 7 | 90.57 | 26.6 |
We can observe joint relationships between these variables in the figure below:
Examination
Among other things, we observe that the Examination variable — the percent of draftees receiving the highest mark on their army exams — has strong negative associations with fertility (Pearson correlation = -0.65), agriculture (correlation = -0.69), and percent Catholic (correlation = -0.57), and a strong positive association with post-primary draftee education rates (correlation = 0.7). It is weakly associated with infant mortality rates (correlation = -0.11).
Looking more closely into this variable, we see that the mean percentage of draftees achieving the top mark is 16% averaging over provinces, and the standard deviation is 8%, indicating a fair amount of dispersion in this percentage across provinces. The values range from 3% to 37%. We can observe this spread in the figure below, which also illustrates the unimodality of the distribution.
