The Relationship between Criminal Activity, Deterrence, Unemployment and Education in England - Case Study Example

The Relationship between Criminal Activity, Deterrence, Unemployment and Education in England and Wales – 1991 Table of content Data description 3 Statement of the problem 4 Hypothesis 4 Descriptive statistics 4 The scatter plot 5 Correlation analysis 6 Regression model of the form (excluding the ED variable): 8 Interpret the R2 statistic and test if it’s statistically significant. 10 The regression model including the ED variables 10 Conclusion 12 The data set 12 Bibliography: 13 Introduction In this study, we are interested in determining if there is any relationship between the criminal activities and independent variables deterrence, unemployment and education in wales and England. There has been considerable interest in the relationship between criminal activity, deterrence variables and social deprivation. Burglary represents one of the main acquisitive crimes in England and Wales. The data reported below are drawn from forty-two police force areas in England and Wales for the year 1991. A persistent theme in economics is that individuals respond to incentives: the purpose of this project is to explore the extent to which judicial penalties (sentencing, probability of a conviction) deter criminal activity and whether crime is related to social problems. Data description The data used in this study was obtained in the city of England and wales. the relationship between the dependent variable BR and the independent variables CR, percentage of crime solved by in the police force area, SEN, average sentence length dispensed by the judiciary in the police force area, UR male unemployment rate in the police force area, HO, percentage of the population in the police force area with higher education, and ED percentage of the population in the police force area with higher education. The data consist of the following variables; BR = Burglary rate per 1000 of the Police Force Area Population. CR = Percentage of crimes solved by in the Police Force Area. SEN = Average sentence length (in months) dispensed by the judiciary in the Police Force Area. UR = Male unemployment rate in the Police Force Area. HO = Percentage of households with three rooms or less in the Police Force area ED = Percentage of the population in the Police Force Area with higher education Statement of the problem In this project we are interested in determining if there is any relationship between the dependent variable burglary rate and independent variables. The project will utilize the regression analysis, and correlation analysis Hypothesis Ho: there is no relationship between the dependent variable burglary rate and the independent variables. H1: there is relationship between the dependent variable burglary rate and the independent variables. Descriptive statistics The summary statistics BR   CR   SEN   UR   HO   ED   Mean 21.69381 Mean 25.71429 Mean 11.39524 Mean 10.09048 Mean 11.49333 Mean 12.97262 Standard Error 1.261976 Standard Error 1.249988 Standard Error 0.210413 Standard Error 0.470374 Standard Error 0.473369 Standard Error 0.403085 Median 19.94 Median 25.5 Median 11.3 Median 9.5 Median 10.925 Median 12.175 Standard Deviation 8.178536 Standard Deviation 8.100845 Standard Deviation 1.363631 Standard Deviation 3.048375 Standard Deviation 3.067784 Standard Deviation 2.612292 Sample Variance 66.88846 Sample Variance 65.62369 Sample Variance 1.859489 Sample Variance 9.29259 Sample Variance 9.411296 Sample Variance 6.824069 Kurtosis 0.998838 Kurtosis -0.52804 Kurtosis -0.65439 Kurtosis 1.435976 Kurtosis 11.88423 Kurtosis 0.721419 Skewness 1.06682 Skewness 0.137739 Skewness 0.18193 Skewness 1.127573 Skewness 2.800292 Skewness 0.99478 Range 36.14 Range 31 Range 5.4 Range 14.7 Range 18.29 Range 11.27 Minimum 10 Minimum 11 Minimum 8.8 Minimum 4.9 Minimum 7.81 Minimum 9.39 Maximum 46.14 Maximum 42 Maximum 14.2 Maximum 19.6 Maximum 26.1 Maximum 20.66 Sum 911.14 Sum 1080 Sum 478.6 Sum 423.8 Sum 482.72 Sum 544.85 Count 42 Count 42 Count 42 Count 42 Count 42 Count 42 The above summary statistics show that the mean BR is equal to 21.69, the standard deviation is equal to 8.179, kurtosis value is 0.9988 and the median is equal to 19.94. From the kurtosis value, the BR data is skewed to the right. The summary statistic of the CR show that the mean of 25.71, the standard deviation is 8.10, the median CR is equal to 11.3, the variance of the CR is equal to 1.859, and the kurtosis is equal to -0.65. From kurtosis value we can conclude that the CR value is skewed to the left. The summary statistic of the SEN has a mean of 11.395, the standard deviation of 1.3636, the median is equal to 11.3, the value of kurtosis is -0.528, and the skewness statistic is equal to 0.1819. From the skew ness value we can say the SEN values are skewed to the right. The summary statistics of the UR indicate a mean value of 10.09, the median is equal to 9.5, the standard deviation is equal to 3.049, the kurtosis is equal to 1.436, and the skew ness statistic value is 1.1276. The summary statistics of ED are, mean value is 12.97, the median is 12.175, the standard deviation is 2.612, the kurtosis is equal to 0.7214, and the skewness statistic is equal to 0.9948. From the skew ness statistic, we can conclude that the HO is skewed to the right The scatter plot From the scatter plot, we can observe that the relationship between the BR and the CR is relatively not significant. Since the regression line has a slope that almost has a zero slope. The scatterplot also show that the variable Br and the SEN has a negative relationship. The scatter plot also indicates the relationship between the variable BR and the UR show a positive relationship. This is because there is a positive slope between the dependent variable Br and the independent variable UR. The scatterplot show that there is a positive relationship between the dependent variable BR and the independent variable HO. This is because the scatterplot show that there is a positive slope. The scatterplot show that there is a positive relationship between the dependent variable BR and the independent variable ED. This is because there is a positive slope between the dependent variable BR and the independent variable ED. Correlation analysis The table of pairwise correlation between the dependent variable BR and the independent variables Correlations: BR CR SEN UR HO CR -0.011 0.943 SEN -0.149 -0.385 0.347 0.012 UR 0.599 0.38 -0.105 0 0.013 0.507 HO 0.296 -0.469 0.267 0.107 0.057 0.002 0.088 0.502 ED -0.442 -0.529 0.339 -0.675 0.353 0.003 0 0.028 0 0.022 Cell Contents: Pearson correlation P-Value From above correlation matrix, we can observe that the value of the correlation between the BR and the CR is -0.011 which has a significant value of 0.943. From this value we can conclude that there is no correlation between the BR and CR. From correlation analysis, the value of correlation between the BR and SEN is equal to -0.149 which a significant value of 0.347. This means that there exist correlation between the BR and the SEN. The correlation value between the UR and the BR is equal to 0.599 with a significant value of 0.000. This means that there is correlation between the BR and the variable UR. The value of the correlation between the BR and the HO is equal to 0.296 which has a significant value of 0.057. This means that there is no correlation between the BR and the variable Ho. From the correlation analysis, we observe that the value of the correlation between the BR and the ED is equal to -0.442 which has a significant value of 0.003. This means that the variable BR and the ED are correlated. Regression model of the form (excluding the ED variable): BRi =α + β1CRi + β2SENi +β3HOi + β4URi + ui where the i subscript corresponds to Police Force Area i, Interpret the coefficients estimates and comment on their economic and statistical significance. SUMMARY OUTPUT Regression Statistics Multiple R 0.693558 R Square 0.481023 Adjusted R Square 0.424918 Standard Error 6.202126 Observations 42 ANOVA   Df SS MS F Significance F Regression 4 1319.171 329.7928 8.573536 5.32E-05 Residual 37 1423.256 38.46637 Total 41 2742.427         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 21.75097 11.55689 1.882078 0.067709 -1.66552 45.16746 CR -0.28201 0.161512 -1.74608 0.089097 -0.60927 0.045242 SEN -1.36381 0.774034 -1.76195 0.08634 -2.93215 0.204536 UR 1.78397 0.366648 4.865619 2.14E-05 1.04107 2.526869 HO 0.411923 0.383191 1.074979 0.289344 -0.3645 1.188342 From the regression model, we can observe that the coefficient of the CR variable is -0.2820, which has a t- statistic of -1.7461 and a p- value of 0.089. This means that the CR variable is not significant to predict the BR dependent variable. The variable SEN has a T- statistic equal to -1.762 with a p- value of 0.086, which mean that the SEN variable is not significant at to predict the dependent variable BR. The variable UR has a t- statistic equal to 4.865 which has a p- value of 0.0000. This mean the independent variable UR is significant to be in the model. The variable HO has a t-statistic of 1.075 which has a p- value of 0.289. This means that the variable HO cannot be used to predict the dependent variable BR. Interpret the R2 statistic and test if it’s statistically significant. Regression Statistics Multiple R 0.693558 R Square 0.481023 Adjusted R Square 0.424918 Standard Error 6.202126 Observations 42 From the regression statistics, we can observe that the value of R- squared is equal to 0.481. This means that the regression model can only be able to control 48.1% of the errors in the model. The value is too low and hence it not statistically significant. The regression model including the ED variables Regression Statistics Multiple R 0.72289 R Square 0.52257 Adjusted R Square 0.45626 Standard Error 6.030748 Observations 42 ANOVA   df SS MS F Significance F Regression 5 1433.11 286.6219 7.88074 4.28E-05 Residual 36 1309.317 36.36992 Total 41 2742.427         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 35.20319 13.56639 2.594883 0.013605 7.689276 62.71711 CR -0.29493 0.157219 -1.87593 0.068791 -0.61379 0.023923 SEN -1.0382 0.774802 -1.33995 0.188658 -2.60957 0.533175 UR 1.138336 0.510062 2.231759 0.031946 0.103882 2.17279 HO 0.756682 0.420444 1.799719 0.080291 -0.09602 1.609382 ED -1.10063 0.62184 -1.76996 0.085203 -2.36178 0.160517 The omission of the ED variable lead to lowing of the R- square value which is less that than the one obtained. This means that the regression model containing the ED is significantly better than the regression model than does not contain the ED variable. Conclusion From the two models, we observe that both regression models can be able to predict the burglary rate. We also observe that the only variable that is significant in the two regression model is the variable of Male unemployment rate in the Police Force Area which is UR. The data set BR CR SEN UR HO ED 23.73 15 9.6 9.1 12.34 14.84 24.09 12 11.7 9.1 12.07 13.56 17.76 29 12.2 7.4 11.93 16.46 17.12 29 10.5 8.7 8.95 15.49 30.99 37 11 16.8 10.97 9.57 22.11 32 8.8 7.2 9.12 12.99 19.69 22 14.1 9.8 9.08 11.85 16.97 20 9.4 11.2 12.72 12.23 14.01 33 10.3 9.6 13.84 13.95 22.45 25 12.5 13.3 10.72 10.36 16.13 26 13.3 9.9 12.71 11.3 23.39 21 12.8 7.3 11.85 15.76 38.15 33 9.6 12.1 12.27 11.42 18.77 20 11.3 9.2 12.61 14.19 11.01 24 14.2 7.4 13.39 17.56 37.68 26 11.3 12.5 10.71 9.73 17.24 16 12 9.9 12.03 12.12 17.78 39 9.9 9.6 10.97 12.04 24.16 25 11.2 8.2 9.91 12.45 15.17 35 10.1 9.3 8.37 10.42 23.32 41 12.2 19.6 11.79 10.4 28.30 11 13.1 10.5 26.1 17.51 20.19 29 11.4 8.4 9.72 11.02 20.69 28 12.5 7.8 9.22 11.93 46.14 29 10.9 16 15.46 10.66 17.11 20 11.3 6.3 10.28 15.54 30.10 22 10.2 11.5 10.42 11.3 27.28 27 11 15.4 10.88 9.91 22.46 33 10.6 9.4 8.36 10.76 11.54 20 10.8 6.7 9.73 12.48 11.04 15 13.7 4.9 12.7 20.66 18.51 12 12.7 9.4 16.56 15.04 17.27 14 11.6 6.6 12.33 18.71 21.00 22 11.9 7.7 9.63 14.59 13.29 33 12.5 8.4 9.98 13.64 32.11 28 10.9 13.4 12.54 9.39 38.05 22 11.2 11 15.5 11.63 14.19 25 9.4 7.6 10.2 13.69 10.00 42 9.5 9.6 7.81 12.69 16.73 40 10 12.3 8.89 10.92 15.58 27 13.2 10 9.11 12.09 27.84 21 12.2 13.7 8.95 12 Variables: BR = Burglary rate per 1000 of the Police Force Area Population. 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