Analysis of Income, Credit Balance, Size, and Location: AJ Davis - Statistics Project Example

Statistics project paper part A Program: Supervisor: May 16, Statistics project paper part A Introduction Statistical applications are important to business organizations for understanding trends, occurrences, and relationships between variables. A department store like AJ Davis that has many credit customers needs to understand demographic factors of the customers, trends in the factors, and relationship of the factors with respect to credit card usage and balances in order to improve management of the customers’ needs and to moderate application of credit cards by the customers. This paper reports on analysis of income, credit balance, size, and location. Descriptive statistics Income variable Income is one of the factors to the company’s credit card users and is important in customer relationship management. The variable has a mean of 43480 and a median of 42000 and closeness between the 2 values means that they are reliable estimates of income of the company’s customers who use credit cards. The variable has a standard deviation of 14550, a value that identifies average deviation of data from the variable’s mean and suggests that the variable concentrate within its second and third quartiles. Consequently, the company can assume that its customers have an average income of $ 43480. The following line graph shows the distribution by cases. Graph 1: Distribution of income of credit card users The graph shows distribution of the variable about the mean value and implies need for general focus on all credit card holders because of an almost normal distribution of the user’s income across the mean. Credit balance variable Credit balance is another variable to the company as it identifies customers’ ability to meet their credit obligations. The following table summarizes some of the statistics for credit balance of the company’s customers. Statistic Value Mean 3964.06 Median 4090 Standard deviation 933.494 Range 3814 The mean represents average values and the organization can assume that its customers have a credit balance of $ 3964.06, a value that is good enough to develop confidence in customer’s ability to use their credit cards for purchases. Even though the median is different from the mean, the percentage difference is small, barely 3 percent, and this means a significant level of reliability of any of the values for estimating credit card balance level of a customer. Such a prediction must however be done with caution because of the high value of range (3814) that means a wide distribution of the customers’ credit card balances. This means that values exist on both extremes and decisions based on customers’ credit card balance must incorporate this in order to meet each of the customers’ interests. The standard deviation however induces a confidence because despite the range, it shows that average deviation is not far from the mean. Consequently, the organization can gamble in accommodating its customers with low credit card balances in its decisions because the high concentration of values about the mean will help to reduce associated risks of such decisions, as could emerge from effects of data at extreme values. The following scatter plat shows the distribution of the customers’ credit card balance, based on case numbers. Graph 2: Scatter plot for distribution of credit card balance The graph shows an even distribution of the balances across the mean or median values that are relatively close. The graph further explains the distribution of the values between $ 2000 and $ 4000. There is however an outlier value, a single value falling outside this range, and it would be advisable to eliminate it when consucting inference analysis because it could induce bias. Size variable The number of people living in a household is another significant factor to the store. This is because of its implications on demand and potential effects on credit card balance and ability to meet credit obligations. The following table summarizes some of the variable’s descriptive statistics. Table 3: Selected descriptive statistics for household size Statistic Value Mean 3.42 Median 3 Standard deviation 1.74 Range 6 The mean suggest an average household size of 3.42. The variable is however discrete and this suggests suitability of the median over the mean in estimating household size. Consequently, household size of the store’s credit card holders can be estimated at three. There is however limited confidence in the estimate because of the high value of standard deviation, relative to the median or mean value. The range is also wide (6) relative to the measures of central tendency (mean= 3.42, median= 3). This means sparse distribution of the variable and the measures of central tendency would not be appropriate statistics as they may mislead the store in estimating household size of a credit card holder. It may also be risky to rely on the measures of central tendency in making decisions on household size because of threat to reliability of applied estimation. The following scatter plot shows the distribution of household size by case number. Graph 3: Distribution of household size The plot supports reliability threat to measures of central tendency because of the lack of pattern in the variable’s distribution. Even though the variable is sparcely distributed, its distribution does not identify possible outlier. An alternative measure of central tendency (median= 2) could therefore be a better measure because the plot demonstrate significant concentration of data at the value. Relationships Relationship between income and location There is a possible relationship between a customer’s location and income. Urban areas are for example associated with greater economic opportunities that would empower people to higher level income that in rural and suburban areas. Similarly, life in urban areas is expected to be more expensive than in other areas and this would mean that people with higher income stay in urban areas. This leads to the following set of hypotheses HO: µurban = µSuburban = µrural: There is no significant difference between the means of income across the three locations HA: µurban ≠ µSuburban ≠ µrural: there is a significant difference between the means of income across the three locations The following table shows the means of income distribution across the three locations. Table 4: Means of income across locations (in thousands) Report income location Mean N Std. Deviation 1 44.1905 21 14.72284 2 50.6667 15 15.25810 3 34.7143 14 8.40722 Total 43.4800 50 14.55074 The results suggest possible difference in the means with highest incomes in suburban areas followed by urban areas and then rural areas. A possible correlation can also be explored between the two variables as shown below. Table 5: Correlation between income and location Correlations location income location Pearson Correlation 1 -.232 Sig. (2-tailed) .105 N 50 50 income Pearson Correlation -.232 1 Sig. (2-tailed) .105 N 50 50 The results show a negative correlation between income and location (-0.232) and this means that as one moves from urban (1) to semi urban (2) to rural (3), income is expected to reduce. The correlation is however not significant (p= 0.105> 0.05) and this means that the observed correlation could be attributed to chance. The following table shows analysis of variance results for test of the hypothesis. Table 6: ANOVA results ANOVA income Sum of Squares df Mean Square F Sig. Between Groups 1861.051 2 930.526 5.137 .010 Within Groups 8513.429 47 181.137 Total 10374.480 49 Analysis of variance however identifies a significant difference in mean of income across the three locations. This is because of the low p-value (0.01< 0.05) and leads to rejection of the above null hypothesis. The analysis of variance results are consistent with the observed differences in means and therefore mean that customers from suburban areas have the highest incomes, followed by those from urban areas, and then those from rural areas have the lowest incomes. The trend also explains lack of correlation because it is non-linear. Consequently, the store can apply segmentation on its customers based on income and may use such strategies as price based branding and discriminative pricing, based on location, to optimize its revenues. The following graph shows distribution of income across locations. Graph 4: Income by location The graph shows that suburban area has its income concentrated at higher values and this explains its higher mean than urban area. Relationship between income and credit balance Income is one of the factors to demand as it defines consumers’ ability to pay for the goods they desire. This could therefore influence credit card balance in two ways. Higher income could have a positive relationship with an individual’s credit card balance because of ability to top up the card with higher values and the ability to retain the balance at high values. Alternatively, income may also dictate high level purchase with a credit card, resulting in low balances because the card holders have the capacity to pay and even top up the card as its balance runs out and this defines a two sided relationship for test. The following set of hypothesis is therefore proposed for the two variables. H0: β= 0, There is no significant relationship between an individual’s income and his or her credit card balance HA: β≠ 0, There is a significant relationship between an individual’s income and his or her credit card balance Correlation analysis offers a preliminary insight into the relationship and the following table shows results of correlation analysis. Table 6: Correlation analysis results for the relationship between income and credit card balance Correlations income creditbalance income Pearson Correlation 1 .631** Sig. (2-tailed) .000 N 50 50 creditbalance Pearson Correlation .631** 1 Sig. (2-tailed) .000 N 50 50 **. Correlation is significant at the 0.01 level (2-tailed). The table shows a strong correlation between the variables (R= 0.631) that is also positive. In addition, the correlation is significant (p= 0.000< 0.05) and this suggests that an increase in an individual’s income level is associated with an increase in the person’s credit card balance. A regression analysis however offers more information on possible relationships and the following tables show regression analysis results for the relationship between income and credit card balance. Table 7: Model summary Model Summaryb Model R R Square Adjusted R Square Std. Error of the Estimate 1 .631a .398 .386 731.71323 a. Predictors: (Constant), income b. Dependent Variable: creditbalance The adjusted R square value shows that the developed model explains 38.6 percent of the data and this is a significant proportion for accepting the model. Table 8: ANOVA ANOVAa Model Sum of Squares df Mean Square F Sig. 1 Regression 16999744.786 1 16999744.786 31.751 .000b Residual 25699404.034 48 535404.251 Total 42699148.820 49 a. Dependent Variable: creditbalance b. Predictors: (Constant), income The developed model is further significant (F= 31.751, p= 0.000< 0.05) and this means a significant relationship between income and credit card balance. Table 9: Table of coefficients Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 2204.000 329.049 6.698 .000 income 40.480 7.184 .631 5.635 .000 a. Dependent Variable: creditbalance The following model is developed from the analysis. Credit card balance= 2204+ 40.48(Income)+ e, Where e is the error term The coefficient, and the constant term are both significant. A positive relationship is therefore confirmed between income and credit card balance and the following graph justifies this. Graph 4: Relationship between income and credit card balance Relationship between size and credit balance Effects of size on demand also suggest a relationship between size and credit card balance and the following hypothesis is proposed for the relationship. HO: µi are the same for all household sizes, No significant difference in credit card balance across sizes HA: Any mean different, a difference exists in the means The following table summarizes mean for the sizes. Table 10: Mean of credit card balance across household sizes Report creditbalance size Mean N Std. Deviation 1.00 2781.4000 5 271.80655 2.00 3278.2667 15 698.99770 3.00 4023.1250 8 375.39177 4.00 4486.7778 9 701.68935 5.00 4532.8000 5 673.28426 6.00 5032.0000 5 711.98069 7.00 4910.6667 3 356.26722 Total 3964.0600 50 933.49408 The following table summarizes ANOVA results for the differences in the means. Table 11: ANOVA results ANOVA creditbalance Sum of Squares df Mean Square F Sig. Between Groups 26543122.789 6 4423853.798 11.774 .000 Within Groups 16156026.031 43 375721.536 Total 42699148.820 49 The results shows significance of the alternative hypothesis (F= 11.774, p= 0.000< 0.05). consequently, credit card balance differs across household sizes and house holds with six people have the highest credit card balance. This further suggests a linear relationship as shown in the following chart. Graph 6: Relationship between household size and credit card balance The graph shows that households with size six have highests balances. Conclusion Income and credit card balance have systematic distributions and measures of central tendencies can inform decision making on the variables. Customers’ income vary by location and influences individuals’ credit card balances. Credit card balance also varry by household size. Individuals in suburban areas and households with six occupants should therefore be the store’s focus in decision making based on credit card balance. Focus should also be made on individuals’ incomes. Read More