For those who asked – the study I did was informal, so there is no formal write-up. The informal study was based on the following two equations (and I will guide the readers through them, painful as that might be – please go to the end of the two equations for that guidance):
Estimate t-Value
Homicide rate =
Other factors (constant) 12.15924 7.73
Fraction black 4.450619 3.89
Average Income -0.000167 -3.95
Ownership rate -0.053896 -3.93
(percent of variance explained: 34.3%)
Ownership rate =
Other factors (constant) 12.18626 0.57
Fraction adolescent 350.8001 4.02
Fraction urbanized -42.6847 -8.00
Average income -0.00123 -3.29
Education 0.4504 1.67
(percent of variance explained: 80%)
The first equation relates the homicide rate across states to three primary factors: fraction of the population of the state that is black, average income in the state, and the ownerhsip rate of the state. There is a fourth factor, which is everything else, and it is subsumed in an unvarying constant term. To know whether a relationship is statistically significant, we use the t-ratio. A t-ratio of greater than 2 usually signifies significance at 95% level (meaning 95% of the time that relationship will not be zero). In one case, though, I left in a t-ratio of about 1.65 which indicates significance at the 90% level. It is considered marginally significant. The reason for everything here being significant is that I eliminated the non-significant relationships.
The first equation says that state homicide rates are positively related to the fraction of the population that is black and negatively related to average income and, very importantly, negatively related to ownership rates. That is a major contradiction to the study cited.
The second equation relates ownership rates to four factors: the fraction of the population that is adolescent (15-25 range), the fraction of the population urbanized, average income and education. (Again, there are all the other factors which are subsumed in a constant term.) What the second equation indicates is that ownership rates are positively related to the fraction of the population that is adolescent, negatively related to urbanization, negatively related to income, and positively related to education.
The way to view these relationships is to think of them as holding all other things constant. So, in the first equation, homicide rates are negatively related to ownership rates if everything else in the equation is constant. In particular, if ownership rates go up by 10 percentage points (for example, from 40% to 50%) then homicide rates would fall by 0.5 homicides per hundred thousand.
What ties the equations together is that they were estimated jointly through a full-information maximumu likelihood method. (Note: percent of variance explained is the R-square.)
