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.