Criminal Activity and Education in The UK - Statistics Project Example

The Relationship between Criminal Activity, Deterrence, Unemployment and Education in England and Wales - 1991 Project L1022: Assessed work Project Your Name Table of Contents Introduction 2 Literature Review 2 Descriptive Statistics 3 Correlations 7 Statistical Significance of Correlation 7 BR and CR 8 BR and SEN 8 BR and UR 8 BR and HO 9 BR and ED 9 Regression Model excluding the ED Variable 9 The Economic and Statistical Significance of the Estimated Coefficients. 10 The Overall Goodness of Fit of the Model 11 Prediction of Burglary Rate when the Police Solve 30% of Crime 12 Redefining the Regression Model including the ED Variable 12 Conclusions 13 Bibliography 14 Appendix A: Histograms 15 The Relationship between Criminal Activity, Deterrence, Unemployment and Education in England and Wales - 1991 Introduction The purpose of this project is to explore the extent to which judicial penalties (sentencing, the probability of a conviction) deter criminal activity and whether crime is related to social problems. The data set provided for the analysis is drawn from forty-two police force areas in England and Wales for the year 1991. The variables and their definitions are given below: 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. The questions that will be addressed using the provided data are Is there a significant relationship between BR and each of the other variables? Whether CR, SEN, UR and HO can be used for significantly predicting BR. What are the additional effects ED can have on predicting BR? This paper will use descriptive statistics techniques for summarizing the key features of the data. Furthermore, this paper will use correlation and regression analysis techniques for testing the relationship between variables and estimating the regression model for predicting BR. Literature Review The Guardian reported that tougher prison sentences reduce crime, particularly burglary. According to the Guardian, research suggests an increase in sentence length for serious offenders can cut burglaries (Helm & Doward, 2012). A research paper on Male unemployment and crimes in England and Wales by Carmichael & Ward (2010) indicated that there is a systematic positive relationship between most crime and male unemployment regardless of age. Their results indicated that both the youth and adult male unemployment rates are consistently and significantly positively related to burglary, theft, fraud and forgery and total crime (Carmichael & Ward, 2001). According to Machin, Marie & Vujić (2010), crime is significantly related to education, especially in the case of property crimes. They find that criminal activity is negatively associated with higher levels of education. Machin, et al research suggests that improving education can yield significant social benefits and can be a key policy tool in the drive to reduce crime. Descriptive Statistics Table 1 shows the summary statistics of the variables. Table 1: Summary Statistics of the variables (n = 42)   BR CR SEN UR HO ED   (per 1000) (%) (months) (%) (%) (%) Mean 21.69 25.71 11.40 10.09 11.49 12.97 Median 19.94 25.50 11.30 9.50 10.93 12.18 Mode N/A 29.00 12.20 9.60 8.95 11.30 SD 8.18 8.10 1.36 3.05 3.07 2.61 Minimum 10.00 11.00 8.80 4.90 7.81 9.39 Maximum 46.14 42.00 14.20 19.60 26.10 20.66 Range 36.14 31.00 5.40 14.70 18.29 11.27 Skewness 1.07 0.14 0.18 1.13 2.80 0.99 Lower Quartile, Q1 16.79 20.25 10.35 7.90 9.65 11.09 Upper Quartile, Q3 24.14 31.25 12.43 11.43 12.49 14.49 Interquartile Range, IQR 7.35 11.00 2.08 3.53 2.84 3.40 Coefficient of Variation 37.70% 31.50% 11.97% 30.21% 26.69% 20.14% The average burglary rate in England and Wales for the year 1991 was 21.69 (SD = 8.18). About half of the police force area burglary rate was above 19.94. The distribution of the BR variable is positively (right) skewed (skew = 1.07). The average crimes solved was 25.71% (SD = 8.10). About half of the police force area solved above 25.50% of crimes. The CR variable is normally distributed (skew = 0.14). The average sentence length was 11.4 months (SD = 1.36). About half of the police force area average sentence length was above 11.3. The SEN variable is normally distributed (skew = 0.18). The average male unemployment rate was 10.09% (SD = 3.05). About half of the police force area male unemployment rate was above 9.5%. The UR variable is positively skewed (skew = 1.13). The average households with three rooms or less was 11.49% (SD = 3.07). About half of the police force area households with three rooms or less was above 10.93%. The HO variable is heavily positively skewed (skew = 2.80). The average % of the population with higher education was 12.97% (SD = 2.61). About half of the police force area population with higher education was above 12.18%. The ED variable is positively skewed (skew = 0.99). The histograms showing distribution for all the variables are presented in Appendix A. The scatter diagram in figure 1 shows the relationship between burglary rate and % of crimes solved. It illustrates a very weak negative relationship – lower burglary rate appears to be associated with higher % of crime solved. Figure 1: Scatter diagram of burglary rate against % of crimes solved The scatter diagram in figure 2 shows the relationship between burglary rate and average sentence length. It illustrates a weak negative relationship – lower burglary rate appears to be associated with higher average sentence length. Figure 2: Scatter diagram of burglary rate against average sentence length The scatter diagram in figure 3 shows the relationship between burglary rate and male unemployment rate. It illustrates a positive relationship – higher burglary rate appears to be associated with higher male unemployment rate. Figure 3: Scatter diagram of burglary rate against male unemployment rate The scatter diagram in figure 4 shows the relationship between burglary rate and % of household with three rooms or less. It illustrates a positive relationship – higher burglary rate appears to be associated with higher % of household with three rooms or less. Figure 4: Scatter diagram of burglary rate against % of household with three rooms or less The scatter diagram in figure 5 shows the relationship between burglary rate and % of population with higher education. It illustrates a negative relationship – lower burglary rate appears to be associated with higher % of population with higher education. Figure 5: Scatter diagram of burglary rate against % of population with higher education Correlations Table 2 shows the correlation matrix of the variables. The correlation coefficient value of -0.011 indicates no linear relationship between burglary rate and % of crimes solved. The correlation coefficient value of -0.149 indicates very weak negative linear relationship between burglary rate and average sentence length. The correlation coefficient value of 0.599 indicates strong positive linear relationship between burglary rate and male unemployment rate. The correlation coefficient value of 0.296 indicates moderately weak positive linear relationship between burglary rate and % of households with three rooms or less. The correlation coefficient value of -0.442 indicates moderately strong negative linear relationship between burglary rate and % of population with higher education. Table 2: Correlation matrix of the variables (n = 42)   BR CR SEN UR HO CR -0.011 SEN -0.149 -0.385 UR 0.599 0.380 -0.105 HO 0.296 -0.469 0.267 0.107 ED -0.442 -0.529 0.339 -0.675 0.353 Statistical Significance of Correlation Below paragraphs will test the statistical significance of correlation coefficients between BR and each of the other variables. The null and alternate hypotheses for each hypothesis test are H0: ρ = 0 (There is no correlation between the two variables.) H1: ρ ≠ 0 (There is a correlation between the two variables.) The selected level of significance, α is 5% by convention. The selected test is the t Test for the Significant Correlation. The degrees of freedom are df = n – 2 = 42 – 2 = 40 At the level of significance of 0.05 with 40 degrees of freedom, the two-tailed critical values of t are -2.021 and +2.021. Therefore the decision rule will be Reject H0 if t < -2.021 or t > 2.021. Otherwise, do not reject H0. The test statistic is calculated using formula below. BR and CR The test statistic is Decision: Do not reject H0, as the test statistic falls in the non-rejection region, -2.021 < t = -0.071 < 2.021. Conclusion: There is not a significant association between the burglary rate and % of crimes solved. BR and SEN The test statistic is Decision: Do not reject H0, as the test statistic falls in the non-rejection region, -2.021 < t = -0.951 < 2.021. Conclusion: There is not a significant association between the burglary rate and average sentence length. BR and UR The test statistic is Decision: Reject H0, as the test statistic falls in the rejection region, t = 4.732 > 2.021. Conclusion: There is a significant association between the burglary rate and male unemployment rate. BR and HO The test statistic is Decision: Do not reject H0, as the test statistic falls in the non-rejection region, -2.021 < t = 1.958 < 2.021. Conclusion: There is not a significant association between the burglary rate and % of households with three rooms or less. BR and ED The test statistic is Decision: Reject H0, as the test statistic falls in the rejection region, t = -3.117 < -2.021. Conclusion: There is a significant association between the burglary rate and % of population with higher education. Thus, there is a significant association between BR and UR, and between BR and ED. Regression Model excluding the ED Variable A regression model is estimated taking BR as the dependent variable and CR, SEN, HO and UR as the independent variables. The results of the regression analysis are presented in table 3. The equation of the regression model is given by: BR = 21.751 – 0.282CR – 1.364SEN + 1.784UR + 0.412HO Table 3: Multiple regression analysis excluding the ED variable SUMMARY OUTPUT Regression Statistics Multiple R 0.694 R Square 0.481 Adjusted R Square 0.425 Standard Error 6.202 Observations 42 ANOVA   df SS MS F Significance F Regression 4 1319.171 329.793 8.574 0.000053 Residual 37 1423.256 38.466 Total 41 2742.427         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 21.751 11.557 1.882 0.067709 -1.666 45.167 CR -0.282 0.162 -1.746 0.089097 -0.609 0.045 SEN -1.364 0.774 -1.762 0.086340 -2.932 0.205 UR 1.784 0.367 4.866 0.000021 1.041 2.527 HO 0.412 0.383 1.075 0.289344 -0.364 1.188 The Economic and Statistical Significance of the Estimated Coefficients. The slope coefficient of CR of -0.282 indicates that for each additional % of crimes solved the mean burglary rate decreases by about 0.282 given the other variables are constant. The slope coefficient of CR is not statistically significant at the significance level of 5% (p-value = 0.089). The slope coefficient of SEN of -1.364 indicates that for each additional month sentence dispensed the mean burglary rate decreases by about 1.364 given the other variables are constant. The slope coefficient of SEN is not statistically significant at the significance level of 5% (p-value = 0.086). The slope coefficient of UR of 1.784 indicates that for each additional % increase in the male unemployment rate the mean burglary rate increases by about 1.784 given the other variables are constant. The slope coefficient of UR is statistically significant at the significance level of 0.1% (p-value < 0.001). The slope coefficient of HO of 0.412 indicates that for each additional % increase in households with three rooms or less the mean burglary rate increases by about 0.412 given the other variables are constant. The slope coefficient of HO is not statistically significant at the significance level of 5% (p-value = 0.289). The Overall Goodness of Fit of the Model The coefficient of determination, R2 value of 0.481 suggests that about 48.1% of the variation in the burglary rate is explained by the CR, SEN, UR and HO variables. Thus, collectively, the CR, SEN, UR and HO variables have a moderately strong effect on the BR variable. To test if the R2 statistic is statistically significant, the null and alternate hypotheses are H0: R2 = 0 H1: R2 > 0 The selected level of significance, α is 5% by convention. The selected test is the F Test for Overall Significance. From table 3, the test statistic, degrees of freedom (df1 and df2) and p-values are F(4, 37) = 8.574 p-value < 0.0001 Decision: Reject H0, as the p-value < 0.0001. Conclusion: The R2 statistic is statistically significant. In other words, the overall goodness of fit of the model is statistically significant. Prediction of Burglary Rate when the Police Solve 30% of Crime An estimate (prediction) of the burglary rate when the police solve 30% of crimes, assuming the other independent variables are at their mean is BR = 21.751 – 0.282(30) – 1.364(11.40) + 1.784(10.09) + 0.412(11.49) = 20.48 An estimate of the burglary rate when the police solve 30% of crimes is about 20.48. Redefining the Regression Model including the ED Variable A regression model is estimated taking BR as the dependent variable and all other variables as the independent variables. The results of the regression analysis are presented in table 4. The equation of the regression model is given by: BR = 35.203 – 0.295CR – 1.038SEN + 1.138UR + 0.757HO – 1.101ED Table 4: Multiple regression analysis including the ED variable SUMMARY OUTPUT Regression Statistics Multiple R 0.723 R Square 0.523 Adjusted R Square 0.456 Standard Error 6.031 Observations 42 ANOVA   df SS MS F Significance F Regression 5 1433.110 286.622 7.881 0.000043 Residual 36 1309.317 36.370 Total 41 2742.427         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 35.203 13.566 2.595 0.013605 7.689 62.717 CR -0.295 0.157 -1.876 0.068791 -0.614 0.024 SEN -1.038 0.775 -1.340 0.188658 -2.610 0.533 UR 1.138 0.510 2.232 0.031946 0.104 2.173 HO 0.757 0.420 1.800 0.080291 -0.096 1.609 ED -1.101 0.622 -1.770 0.085203 -2.362 0.161 In this regression model, the value of the slope coefficients of the variables SEN and HO is increased and CR and UR is decreased. The coefficient of determination, R2 value of 0.523 is higher and the overall significance p-value is lower in this regression model indicating the superior goodness of fit as compared to the earlier model excluding the ED variable. Thus, this model gives better goodness of fit as compared to the earlier model. Furthermore, the slope coefficient of ED of -1.101 indicates that for each additional % increase in population higher education the mean burglary rate decreases by about 1.101 given the other variables are constant. The slope coefficient of ED is not statistically significant at the significance level of 5% (p-value = 0.085), however, it is significant at the significance level of 10%. This suggests that the omission of ED in the earlier regression model may have somewhat biased the results. Thus, the ED variable can have an effect on predicting BR. Conclusions The average burglary rate per 1000 of the police force area populations in England and Wales for the year 1991 was 21.69 and vary from the mean by about 8.18. There is a significant strong positive association between burglary rate and male unemployment rate indicating the higher male unemployment rate leads to higher burglary rate. Furthermore, there is a significant negative association between burglary rate and percentage of population with higher education indicating higher education leads to lower burglary rate. The variables crimes solved, average sentence length, male unemployment rate, households with three rooms or less, and population with higher education can be used for significantly predicting the burglary rate of the Police Force Area Population using a regression model. Male unemployment rate is a significant predictor of the burglary rate in the model. Higher education influences burglary rate, however, it is not a significant predictor in the model. Bibliography Barrow, M., 2013. Statistics for Economics, Accounting and Business Studies. 6th ed. England: Prentice Hall. Carmichael, F. & Ward, R., 2001. Male unemployment and crime in England and Wales. Economics Letters, 14 October, 73(1), pp. 111-115. Helm, T. & Doward, J., 2012. Longer prison terms really do cut crime, study shows. [Online] Available at: http://www.theguardian.com/law/2012/jul/07/longer-prison-sentences-cut-crime [Accessed 9 December 2014]. Machin, S., Marie, O. & Vujić, S., 2010. The Crime Reducing Effect of Education. [Online] Available at: http://ftp.iza.org/dp5000.pdf [Accessed 9 December 2014]. Appendix A: Histograms Read More