Determining what factors affect violent crime arrests in CaliforniaIntroductionSlide 3Executive SummarySlide 5What We ExpectInitial TestSlide 8ResultsSecond RegressionNext stepSlide 12Major Problem!Slide 14Fix our errors!Fix Our ErrorsFinal RegressionDescriptive StatisticsStatistical AnalysisSlide 20ConclusionDetermining what factors affect violent crime arrests in CaliforniaZhengying Cao, Chad Nassif, Corinna Traumueller, Ryan Sturtevant, Jeong-Jun Lee & Liz MontanoIntroduction•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 populationExecutive 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–educationWhat 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 expendituresInitial TestDependent 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) 0.000000Initial Test•The big peak is due to LA county, which is large in comparison to the other California counties.-2000-10000100020003000010000200003000040000500005 10 15 20 25 30 35 40 45 50 55Residual Actual FittedResults•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 RegressionDependent 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) 0.000000Next 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) 0.000000Next step•It seems logical that the towns with higher populations also have higher violent crime.-6000-4000-2000020004000-10000010000200003000040000500005 10 15 20 25 30 35 40 45 50 55Residual Actual Fitted 02000000400000060000008000000100000000 10000 20000 30000 40000 50000VIOLENTCRIMESPOPULATIONMajor 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.0500001000001500002000002500000 200000040000006000000800000010000000POPULATIONP E R S O N A L I N C O M E0100000020000003000000400000050000000 200000040000006000000800000010000000POPULATIONC J E X P E N D I T U R E S050001000015000200000 200000040000006000000800000010000000POPULATIONA L C O H O L A R R E S T S010000200003000040000500000 200000040000006000000800000010000000POPULATIONV I O L E N T C R I M E S05001000150020000 200000040000006000000800000010000000POPULATIONW E A P O N S A R R E S T SFix 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 capitaFix 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