Determining what factors affect violent crime arrests in California Zhengying Cao, Chad Nassif,...
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Transcript of Determining what factors affect violent crime arrests in California Zhengying Cao, Chad Nassif,...
Determining what factors affect violent crime arrests in
California
Zhengying Cao, Chad Nassif, Corinna Traumueller, Ryan
Sturtevant, Jeong-Jun Lee & Liz Montano
Introduction
• What– Want to estimate what factors affect violent
crimes arrests in the state of California.
• Why– We hope to find what particular characteristics
of certain counties cause changes in violent crime arrests throughout the state.
Introduction
• How
– Collect data on each of the 58 counties in California for the year 1998.
– Run a cross sectional multiple regression analysis.
Executive Summary
• Rather than gathering data across time, we will run a cross sectional analysis across counties.
• This will help us determine what particular aspects about counties in California affect violent crime arrests.
• Did violent crime arrests in 1998 depend on unemployment, education, population, expenditures and % minority population
Executive Summary
• Dependent variable– Violent crime arrests
• Independent variables– Unemployment rate
– Weapons arrests
– Alcohol arrests
– County population
– County personal income
– Government expenditures on crime and justice
– % minorities in county population
– education
What We Expect
• Positive Correlation– Unemployment rate
– Weapons arrests
– Alcohol arrests
– Population
– % Minorities in county
• Negative Correlation– Median years in school
– Personal income
– Crime and Justice expenditures
Initial Test
Dependent Variable: VIOLENTCRIMES Method: Least Squares Date: 11/28/02 Time: 17:11 Sample: 1 58 Included observations: 58
Variable Coefficient Std. Error t-Statistic Prob.
C -2132.562 3015.932 -0.707099 0.4829 WEAPONSARRESTS 3.636049 2.002803 1.815480 0.0756
UNEMPLOYRATE 19.75080 30.80192 0.641220 0.5244 POPULATION 0.003619 0.000978 3.701254 0.0005
PERSONALINCOME -0.111548 0.025333 -4.403322 0.0001 PERCENTMPOP 0.385972 7.210695 0.053528 0.9575
MEDIANYRSCHOOL 147.6983 215.5072 0.685352 0.4964 CJEXPENDITURES 0.006619 0.001265 5.232488 0.0000 ALCOHOLARRESTS 0.096608 0.077761 1.242370 0.2200
R-squared 0.993593 Mean dependent var 2486.776 Adjusted R-squared 0.992547 S.D. dependent var 6402.682 S.E. of regression 552.7613 Akaike info criterion 15.60945 Sum squared resid 14971706 Schwarz criterion 15.92918 Log likelihood -443.6741 F-statistic 949.8215 Durbin-Watson stat 1.566242 Prob(F-statistic) 0.000000
Initial Test
• The big peak is due to LA county, which is large in comparison to the other California counties.
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Results
• Inconsistency of t-stat and f-stat may be due to multicollinearity.
• By using backward stepwise regression we were able to form a second regression.
Second Regression
Dependent Variable: VIOLENTCRIMES Method: Least Squares Date: 11/28/02 Time: 17:32 Sample: 1 58 Included observations: 58
Variable Coefficient Std. Error t-Statistic Prob.
C 48.80347 89.35481 0.546176 0.5872 WEAPONSARRESTS 4.692440 1.793629 2.616171 0.0116
POPULATION 0.003551 0.000888 3.998835 0.0002 PERSONALINCOME -0.094750 0.019025 -4.980269 0.0000 CJEXPENDITURES 0.005742 0.000969 5.923130 0.0000
R-squared 0.993269 Mean dependent var 2486.776 Adjusted R-squared 0.992761 S.D. dependent var 6402.682 S.E. of regression 544.7378 Akaike info criterion 15.52075 Sum squared resid 15727180 Schwarz criterion 15.69837 Log likelihood -445.1017 F-statistic 1955.379 Durbin-Watson stat 1.548594 Prob(F-statistic) 0.000000
Next step
• Run violent crimes against population alone to see how well it explains it.
Dependent Variable: VIOLENTCRIMES Method: Least Squares Sample: 1 58 Included observations: 58
Variable Coefficient Std. Error t-Statistic Prob.
POPULATION 0.004640 0.000102 45.66935 0.0000 C -192.5154 149.1742 -1.290540 0.2022
R-squared 0.973852 Mean dependent var 2486.776 Adjusted R-squared 0.973385 S.D. dependent var 6402.682 S.E. of regression 1044.531 Akaike info criterion 16.77440 Sum squared resid 61098476 Schwarz criterion 16.84545 Log likelihood -484.4575 F-statistic 2085.689 Durbin-Watson stat 1.965691 Prob(F-statistic) 0.000000
Next step
• It seems logical that the towns with higher populations also have higher violent crime.
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Major Problem!
• Population seems to be collinear with almost every variable.
• Higher populations are correlated with higher levels of personal income, crime expenditures, weapons arrests and alcohol arrests. That is why our initial regression was such a good model.
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Fix our errors!
• We must hold population constant by using rates, percentages and per capita variables.
• Adjusted Variables– Violent crimes per capita– Per capita personal income– Weapons arrests per capita– Alcohol arrests per capita– Expenditures per capita
Fix Our Errors
• Wald test proves that personal income = unemployment = education.– Therefore will only use one, education.
• Secondly, crime & justice expenditures are dependent on violent crime arrests and violent crime arrests are dependent on crime & justice expenditures.– Therefore we need to either run a two-stage least
squares analysis or eliminate it from the model.
Final RegressionDependent Variable: VIOLENTCRIMEPC Method: Least Squares Date: 11/28/02 Time: 17:40 Sample: 1 58 Included observations: 58
Variable Coefficient Std. Error t-Statistic Prob.
C 0.014360 0.003003 4.782194 0.0000 ALCOHOLARRESTS
PC 0.121383 0.040519 2.995675 0.0041
WEAPONSARRESTSPC
2.017101 0.528170 3.819041 0.0003
EDUCATION -0.000843 0.000220 -3.829540 0.0003
R-squared 0.485361 Mean dependent var 0.004499 Adjusted R-squared 0.456770 S.D. dependent var 0.001389 S.E. of regression 0.001023 Akaike info criterion -10.86489 Sum squared resid 5.66E-05 Schwarz criterion -10.72279 Log likelihood 319.0819 F-statistic 16.97599 Durbin-Watson stat 1.676280 Prob(F-statistic) 0.000000
Descriptive Statistics
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Series: ResidualsSample 1 58Observations 58
Mean 2.21E-18Median -9.08E-05Maximum 0.002705Minimum -0.001940Std. Dev. 0.000996Skewness 0.277164Kurtosis 2.494291
Jarque-Bera 1.360636Probability 0.506456
Statistical Analysis
• When we adjust for population we see that education/per capita personal income/unemployment rate, alcohol arrests per capita and weapons arrests per capita all have an impact on violent crime arrests in the state of California.
Statistical Analysis
• Disregarding multicollinearity, the only insignificant variable seems to be the % of minorities in county population.
• However minorities are correlated with unemployment, education and personal income. – It is usually minorities within a county that are
less educated, unemployed and have less personal income.
Conclusion
• Less employment and less education leads to more miscellaneous & misdemeanor crimes such as alcohol arrests and weapons arrests.
• The more crime in general per county leads to more violent crimes per county.