Robbery trends show an increase from 0 cases in 2010 to 1 case in 2011, followed by a return to 0 in 2013. The robbery rate per 1,000 people went from 0 in 2010 to 0.21 in 2011, then back to 0 in 2013. The city's contribution to state robbery statistics was 0% in 2010, rose to 0.01% in 2011, and returned to 0% in 2013.

Aggravated assault cases fluctuated significantly, with 5 cases in 2010, dropping to 0 in 2011, and then sharply rising to 8 in 2013. The rate per 1,000 people followed this trend, going from 1.13 in 2010 to 0 in 2011, and then to 1.68 in 2013. The city's contribution to state aggravated assault statistics varied from 0.04% in 2010 to 0% in 2011, and then increased to 0.06% in 2013.

Examining correlations, we observe a potential link between population density and violent crime rates. As population density increased from 1,880 per square mile in 2010 to 2,032 in 2013, violent crimes also showed an overall increase. The median rent data is only available from 2013 onwards, limiting our ability to draw correlations with crime trends for the given period.

Applying predictive models based on the limited data available, we can cautiously forecast that by 2029, Sparta may see a slight increase in violent crimes if current trends continue. The aggravated assault rate, in particular, may continue to show volatility.

In summary, Sparta experienced fluctuations in violent crime rates between 2010 and 2013, with notable changes in aggravated assaults and a consistent absence of murders. The city's contribution to state crime statistics remained relatively low across all categories. These trends, coupled with the growing population density, suggest a need for continued vigilance in crime prevention strategies in Sparta.