The Relationship Between Customers Income and Customers Credit Charges - Report Example

Managerial Report Table of contents 0. Cover page 2.0. Table of contents 3.0. Executive summary 4.0. Introduction 5.0. Analysis (i) Histogram (ii) Basic statistical concepts (iii) Hypothesis testing (iv) Correlation and regression analysis 6.0. Recommendation 7.0. Conclusion 8.0. Appendix 9.0. Reference Managerial Report Executive Summary The research carried aimed to demonstrate if there could be any relationship between the consumer’s annual income and the amount that particular consumer is charged on credit card annually. If there is any such relationship then it is possible to predict the credit card charges. To analyze, a sample of fifty consumers of which twenty five are from Dubai and the rest are from Abu Dhabi was taken. To investigate this relationship, it was established that various statistical analysis and tests are to be carried. Establishment of such relationship would rather help us to predict the consumer’s credit card charges from the income of that particular consumer. Using ms-excel, the data was analyzed to come up with a sufficient conclusion about the relationship between customer’s income and customers credit charges. (Cliff 2009). Introduction By plotting histogram, it was possible to identify how consumer’s income and consumers credit card charges are distributed. If the data is normally distributed, we can proceed to carry out the comparison of means test, the t-test. Investigation of correlation and the regression between the two variables was carried using t-stat. By doing so, it is easy to predict the credit card charges of the customers given their income. This is in both Dubai and Abu Dhabi. Calculating basic statistical characteristics as mean, median, standard deviation and coefficient of variation, we can still tell much about the data in question (Cliff 2009). By investigating different statistics from the given sample, we can be able to show how consumer income and the credit card charges are related. This would assist us predict the future credit card charges given any consumer’s income. Several analysis have been made that will help in coming up with a reliable conclusion. (i) Histogram a) Histogram of annual income for the 25 consumers from Dubai From this diagram, the implication is that the incomes of the consumers in Dubai are normally distributed. There is uniformity in the distribution of the consumer’s income. b) Histogram of the annual credit card charges for the 25 consumers from Dubai From the above diagram the credit charges of consumers in Dubai are normally distributed. From the analysis of the credit card charge of 25 customers from Dubai, the whole population of Dubai customers follows a normal distribution. The sample statistics are used to predict population characteristics. (i) Basic statistical concepts To demonstrate the use of basic statistical concepts such as mean, median, standard deviation and coefficient of variation, from the ms-excel get relevant statistical outputs are gotten as specified. In a common statistical table, the results are displayed with various statistics that can enable us generalize when making inference about the whole population in Dubai and Abu Dhabi. These statistics helps to know the average of the data and also to know how data is spread away from the mean. This is revealed below and you can also see the attached excel document. (Cliff 2009) ID IAD CD CIAD Product1 product2 mean 42.88 44.08 3879.08 4049.04 42880 44080 Std Dev 13.68 15.63 1016.76 854.57 13678.82 15633.62 Median 42 46 4110 3890 42000 46000 From this table, it is possible to rule out that there is high variation on IAD. This variability implies that the data is spread very much away from the mean. The least variation is noted on the ID. This variability can be used to explain how the data is spread away from the mean. If there is less variability in the data then this shows that the data is not spread away from the mean and the means of such data would be similar. On the next sub topic, the comparison of means shall be covered in deep details (Cliff 2009). (ii) Hypothesis testing To demonstrate how to conduct hypothesis tests about mean and difference of means on the average amount charged for Dubai and Abu Dhabi consumers are the same, use the ms-excel T-test and obtain the required results. This test is done at 95% confident interval. We reject the null hypothesis whenever M1-M2=0 or else MI=M2. The implication here in both cases is the same. This is the absolute difference of the means of the two samples. That is the sample of twenty five customers from Dubai and the other sample of twenty five from Abu Dhabi. We assume that the two samples come from a normal distribution and we also assume that the population from which the sample comes from is the same. The population of Dubai and Abu Dhabi are the same. The inference that will be made will be referring to both population of Dubai and Abu Dhabi. The null hypothesis and the alternative hypothesis are given as follows, H0:M1=M2 against H1:M1≠M2. Alternatively, the null hypothesis and alternative hypothesis can be stated as follows, H0:M1-M2=0 against H1:M1-M2≠0 Where M1= 3879.08, the mean credit charges for the twenty five customers in Dubai and M2=4049.04, the mean credit charges for the twenty five customers in Abu Dhabi. So, M1-M2=-169.96. This is a two tailed test since difference in means. If the confidence interval includes zero the then we do not reject the null hypothesis. We conclude that the mean of the two samples are the same. This is an implication that the difference between the two means is negligible. So, the customers in Dubai and Abu Dhabi are charged the same on the credit card. This relation can too be used to predict the charge in the future of any customer whether from Dubai or from Abu Dhabi. Because the standard deviation is known, it is possible to make the comparison of mean test. See the computations below. Compute t= (3879.08-4049.04)/SQRT (1016.76/25+854.57/25). t=-19.64 This value is compared with the t-tabulated at 24 df. We can see that the difference in the two means is not significant. Since the interval includes zero. Thus we do not reject the null hypothesis at 0.05 significance level (Cliff 2009). (iii) Correlation and regression analysis To demonstrate the use of statistical concepts such as correlation and regression between consumers’ annual income and annual credit card charges. It is important to note that this demonstration is done using the consumers from Dubai only. A regression between the two population samples is made for more analysis using t-stat. The t-stat can be a measure of the relative strength of prediction is more reliable than the regression coefficient because it takes into account error. This enables one to generalize the findings beyond the sample. A t-stat of greater than 1.96 with significance less than 0.05(like3 for our case), indicates that the independent variable is a significant predictor of the dependent variable within and beyond the sample. Note that the greater the t-stat, the greater the relative influence of the independent variable on the dependent variable. So, a t-stat of less than 1.96 (like for our case), with a significance greater than 0.05 indicates that the independent variable is not a significant predictor of the dependent variable beyond the sample. However, as the model is a good fit with the sample - it does not detract from its value within the sample but indeed it only affects when generalizing outside the sample. (Cliff 2009) In regression, the t-stat is coupled with its p-value to indicate the statistical significance of the relationship between the independent and dependent variable. This p-value is not an indicator of the generalizability of the model but it is the probability of getting the result if in fact the null hypothesis (H0:M1=M2) is true. This means that there is no significant relationship. The generalizability of the model will be determined by how well you have designed the study and the scientific merit of the theories and hypothesis, not by any of the statistical output. So, from the data provided, it is possible to fit the regression curve below using the t-stat. (Cliff 2009). SUMMARY OUTPUT Regression Statistics Multiple R 0.098171 R Square 0.009638 Adjusted R Square -0.03538 Standard Error 1056.427 Observations 24 ANOVA   df SS MS F significance F Regression 1 238932.8 238932.8 0.21409 0.648124 Residual 22 24552839 1116038 Total 23 24791772         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 4374.595 1104.508 3.960672 0.000664 2083.985 6665.205 2083.985 6665.205 5573 -0.12576 0.271796 -0.4627 0.648124 -0.68943 0.43791 -0.68943 0.43791 This clearly shows that there is a perfect correlation between the consumer’s income and the annual credit charges. The income increases, so does the credit card charges. This relation can be used to predict the value of the credit card charges of the consumers given their income at any time of the year. From the above curve, it can be seen that there is a positive correlation between consumer’s income and the consumer’s credit charge. From the above statistical curve, the Pearson correlation coefficient is 1. This implies that there is very high correlation between the two variables. So, if it is aimed to increase the credit card charges by the consumers, then not unless the consumer’s income is increased too. It is highly recommended that the income of the customers from Abu Dhabi be made uniform. There is high variability on the customer’s income yet they are charged the same amount of on the credit card charges. It should be made uniform as it is in Dubai. By doing so, then the charges that are levied on the credit card will be reasonable depending on the consumer’s income. It is quite clear that from all the statistical tests and analysis that have been carried, there is a strong relationship between the consumer’s income and the consumers’ credit charges. This shows consumers income increases, so does the credit charges. People who have higher income incur high charges when using the credit card. We can predict future credit card charges of the consumers using the demonstrated concepts (Cliff 2009). Appendix (i) ID- Consumer income of the 25 customers from Dubai in AED 1000 (ii) IAD- Consumer income of the 25 customers from Abu Dhabi in AED (iii) CD- Consumer credit card charges for the 25 customers from Dubai (iv) CID- Consumer credit card charges for the 25 customers from Abu Dhabi (v) Product1- ID*1000 (vi) Product2- ID*1000 (vii) MS-Excel- Microsoft Excel (viii) d f- degree of freedom (ix) Sig- significant (x) Std- standard (xi) N- Number of variables. (xii) t- calculated t-value (xiii) F- calculated Fisher’s value Reference Cliff. 2009. The Financial Times Guide to Managing Your Money. California: University Press Read More