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.
Assume y=f(x); 0<x<1 and y is non-negative real number.
if cov(x,y)=+ve, then
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?