How to Use Regression Analysis to Investigate the Effect

The research discussed here entails data that was collected from an institution of learning where students thought that the rate of crime in the institution could be associated with the number of students enrolled in the institution and the number of police deployed. This paper aims to investigate two particular research studies: 

Whether the number of police officers is in any way related to the number of crimes. In particular, we want to answer the question, does an increase in the number of crimes prompt an increase in the number of police deployed? 

Does the number of crimes committed relate to the total enrolment? We want to investigate whether an enrolment of a high number of students leads to an increase in the crime rate. 

Research and findings 

A random sample of 30 cases was used in the analysis. In order to address the research questions, we will run a regression analysis to investigate whether a correlation exists using Excel. The data set contains three variables, that is, the number of police officers, which represent the overall number of officers deployed, the number of crimes committed and reported within a particular specified period, and the total number of students enrolled within a stated time. The depended (explanatory) variable to address both the research questions is the number of crimes, while the independent (predictor) variables are the total number of police officers and total enrolment . 

Null hypothesis H 0 : There is no association between the number of crimes and the number of police officers. 

Alternative hypothesis H a : There is a statistically significant association 

Null hypothesis H 0 : There is no significant association between the number of crimes committed and the total enrolment. 

Alternative hypothesis H a : there is a significant association 

Analysis 

Descriptive statistics for the number of crimes 

Number of rimes
Mean	160.1
Standard Error	9.316695
Median	167
Mode	205
Standard Deviation	51.02964
Sample Variance	2604.024
Kurtosis	-1.13935
Skewness	0.022443
Range	163
Minimum	85
Maximum	248
Sum	4803
Count	30
Confidence Level (95.0%)	19.05478

From the descriptive table above, the mean number (average value) of crimes committed is 160.1 (Smith, 2011). The median is 165, while the mode which is the most repeated value is 205. According to Coolidge and Coolidge (2012) , the range is the difference between the highest and the lowest value, which in this case is 163. The Crime number is weak positively skewed at 0.022443. The skewness is not statistically significant since the value lies between -1 and 1 (Moy, Chen, & Kao, 2015) . 

When the standard deviation is low, it means that data points are very close to the average/mean; a high standard deviation means that the points of the data are spread over a considerably large range of values (Jackson, 2016). In our case, the standard deviation (51.02964) is considerably low indicating that the data points are close to the mean. 

Descriptive statistics for the number of police officers 

Number of police
Mean	58.7
Standard Error	5.763969
Median	64
Mode	16
Standard Deviation	31.57056
Sample Variance	996.7
Kurtosis	-1.25476
Skewness	-0.02075
Range	98
Minimum	12
Maximum	110
Sum	1761
Count	30

The mean number of police officers is 58.7, while the median is 64. The mode, which is the most repeated value from the descriptive table above is 16. 

The standard deviation (31.57056) is low indicating that the data points are close to the mean (Ghilani & Wolf, 2010). 

The skewness value is -0.02075, which shows that the data is weakly negatively skewed. 

Descriptive statistics for the total enrolment 

Total enrollment
Mean	21368.5
Standard Error	1847.531
Median	18047
Mode	#N/A
Standard Deviation	10119.34
Sample Variance	1.02E+08
Kurtosis	-1.06326
Skewness	0.246729
Range	34988
Minimum	4030
Maximum	39018
Sum	641055
Count	30

The mean number of students enrolled is 21368.5, while the median is 18047. The mode does not exist since all the values appeared once. The data is weakly positively skewed with a value of 0.246729. The data points are close to the mean since the standard deviation is low. 

A scatter plot of the number of crimes against the number of police 

Scatter plot of the number of crimes committed against the total enrollment 

Regression analysis for the number of crimes and number of police 

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.077236
R Square	0.005965
Adjusted R Square	-0.02954
Standard Error	52.06715
Observations	30
ANOVA
	df	SS	MS	F	Significance F
Regression	1	455.5426	455.5426	0.168036	0.684983
Residual	28	75907.66	2710.988
Total	29	76363.2
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	174.4155	23.95973	7.279528	6.33E-08	125.3362	223.4948	125.3362	223.4948
Number of police	-0.17923	0.437241	-0.40992	0.684983	-1.07488	0.716413	-1.07488	0.716413

From the findings, the p-value is 0.684983 which is greater than the 0.05% significant level. We, therefore, fail to reject the null hypothesis of no association between the two variables (Wilcox, 2012). Furthermore, the correlation coefficient value is 0.005965, indicating that a very weak positive association exist between the two variables further supporting our finding (Sharma, 2012). The graphs above also indicate the same. We, therefore, conclude that there is no significant association between the number of crimes committed and the number of police deployed. In other words, the crime rate is very independent of the number of police officers. 

Regression analysis for the number of crimes and the total enrollment 

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.079587
R Square	0.006334
Adjusted R Square	-0.02915
Standard Error	56.37233
Observations	30
ANOVA
	df	SS	MS	F	Significance F
Regression	1	567.1925	567.1925	0.178484	0.675906
Residual	28	88979.51	3177.84
Total	29	89546.7
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	157.5454	20.22321	7.790328	1.74E-08	116.1201	198.9708	116.1201	198.9708
Total enrollment	0.000373	0.000882	0.422473	0.675906	-0.00143	0.00218	-0.00143	0.00218

From the finding or the results above, it can be clearly deduced that the p-value is 0.675906 which is way greater than the 0.05% level of significance. We cannot reject the null hypothesis in this case of no association between the number of crimes and the total enrolment variables (Goos & Meintrup, 2016) . Moreover, the correlation coefficient value from the summary output is 0.006334, indicating that a weak positive relationship exists between the two variables further supporting our finding. The graphs above also prove the same. We can, therefore, make a conclusion that there is no significant association between the number of crimes committed and the total enrollment. In other words, the rate of crime is not influenced by the enrollment number of the students; an increase in the number of students admitted does not necessarily mean that it would result in an increase in the number of crimes. 

The reason as to why I used the regression analysis method is because it gives a clear picture or a good understanding of the depended variables that are related to the independent variables, and also to show the type of relationship that exists (Darlington & Hayes, 2017). Regression analysis is very important in this case since we are interested in examining a continuous dependent variable to see whether it can be predicted from the independent variables. At the same time, regression analysis is useful in showing the causal association between the dependent and the independent variable. Two variables are said to have a causal relationship or association if the occurrence of one event affects the occurrence of the other event (Beri, 2013). In this case, the event that occurs first is called the cause, while the second event is normally referred to as the effect. 

Conclusion 

From the research that has been carried out here, based on the findings, it is pretty clear that although most students in the research study area tend to think that whenever the rate of crime is high, then more police officers are deployed in the institution and that whenever there is high enrollment, then consequently the rate of crime increases, the results prove otherwise. Both variables are independent of the number of crimes. 

References  

Beri, G. C. (2013).  Marketing research . New Delhi: Tata McGraw-Hill. 

Coolidge, F. L., & Coolidge, F. L. (2012).  Statistics: A Gentle Introduction: A Gentle Introduction . Thousand Oaks, CA: SAGE. 

Darlington, R. B., & Hayes, A. F. (2017).  Regression analysis and linear models: Concepts, applications, and implementation . New York, NY: The Guilford Press. 

Ghilani, C. D., & Wolf, P. R. (2010).  Adjustment Computations: Spatial data analysis. Hoboken, NJ: Wiley. 

Goos, P., & Meintrup, D. (2016).  Statistics with JMP: Hypothesis tests, ANOVA, and regression . Chichester, West Sussex: John Wiley & Sons. 

Jackson, S. L. (2016).  Research methods and statistics: A critical thinking approach (5th ed.). Boston, MA: Cengage Learning. 

Moy, R. L., Chen, L.S., & Kao, L. J. (2015).  Study guide for statistics for business and financial economics: A supplement to the textbook by Cheng-Few Lee, John C. Lee and Alice C. Lee . 

Sharma, J. (2012).  Business Statistics . Pearson Education India 

Smith, G. (2011).  Essential Statistics, Regression, and Econometrics . Cambridge, MA: Academic Press. 

Wilcox, R. R. (2012).  Introduction to Robust Estimation and Hypothesis Testing . Academic Press.