# Interpreting the regression results

This might be a basic question. The article given below checks the relationship between crime and income inequality. https://www.sciencedirect.com/science/article/pii/S0165176508001110. Both crime and gini is log transformed.

Table 1 shows -0.6942 as the coefficient for regressing crime on income inequality. There are other values for different types of crime but let's focus on violent crime in Table 1. The interpretation of the results is states as follows "So when Gini ratio increases by 1%, violent crime increase by 0.6942%"! I am not able to understand the interpretation since the coefficient is negative.

My thoughts:

Assume y=f(x); 0<x<1 and y is non-negative real number.

if cov(x,y)=+ve, then

cov(ln(x),y)=E(ln(x)y)-E(ln(x))*E(y);

since ln(x) is negative first term is negative. the second term is also negative as E(ln(x)) is negative. However, I am not sure whether the outcome is +ve or -ve? Is it inconclusive?

• It is true that $ln(Gini)<0$ because $Gini<1$. But some Stata simulations don't convincee me that this necessarily explains the result. clear all set obs 100 gen x = runiform() gen y = 2*x + runiform() gen lnx = ln(x) gen lny = ln(y) reg lny lnx Jan 10 at 14:31