Consumer Research Stats Case Analysis

Consumer Research, Inc. is investigating whether there is any correlation between specific characteristics of credit card users and the amount these users charge on credit cards. Their objective is to determine if these characteristics can accurately predict the annual dollar amount charged by credit card users. Data was collected from a sample of 50 credit card consumers presenting information on the annual income (referred as Income), size of household (referred as Household), and the annual credit card charges (referred as Charges) for these consumers. A statistical analysis; including a descriptive, simple regression, and multiple regression tests, of this data was performed and the findings are presented below. Due to the uncertainty of the size of the intended population with respect to the size of the sample data, any inferences implied from this analysis are merely observations and should not be applied as absolute findings with regards to the entire credit card consumer population.

Descriptive statistics was performed for each of the three characteristics (variables), Charges, Income, and Household, from the survey. The sample data reveals the average credit card user has an Income of $43,480, a Household consisting of 3.4 people, and has $3,964 in credit card Charges. To determine if a relationship exists between Charges and Income, or Charges and Household, a scatter plot graph illustrates a positive relationship for both consumer characteristics (Exhibit 1). However, there is no apparent relationship between Income and size of Household. This finding clarifies that the two characteristics are indeed independent of each other and are good variables to use in determining multiple characteristic effects on credit card charges.

Furthermore, the strength of the relationship between Charges and Income, and Charges and Household is relatively strong. Reviewing the correlation coefficients, Household appears to have a slightly stronger relationship to the amount charged with a .75 correlation compared to Income's correlation strength of .63.

In performing just a basic descriptive analysis of the data, it would appear that a consumer's annual income could be used as an indicator of how much they will charge on a credit card. This is consistent with beliefs that the more money a person makes the more likely they will spend. It is also not surprising to see consumers who reside in larger households will spend more. Further investigation of each of these characteristics was performed using a simple regression analysis to determine if either of these two characteristics could be used to predict the annual credit card charges. Results from this analysis are consistent with the findings of the descriptive analysis and support that, individually, Income and Household do have a positive relationship with credit card charges. A summary of the findings from the simple regression analysis follows.

Annual Income's relationship and strength of predictability for Annual Charges:

A model equation of Annual Charges = 40.48x + 2,204 can be used to predict the annual credit card charges based on just the consumer's annual income. The model indicates that for with each additional $1000 dollars of Income, Charges are expected to increase by $40.48, when the Size of Household is held constant. This model produces the following statistical evidence:

Model Summary of using Income to predict Charges

R RІ Adjusted RІ Std Error of Estimate

.631 0.398 0.386 731.713

Paying particular attention to the RІ values (Table 1), this prediction equation can only account for about 38.6% of the variations present within the data. In other words, there is not a significant explanation for the variability of the amount charged with respect to a consumer's income. Ideally, we would like to explain most if not all of the original variability.

Household Size's relationship and strength of predictability for Annual Charges:

A model equation of Annual Charges = 404.128x + 2,204 can be used to predict the annual credit card charges based on just the size of the consumer's household. The model indicates that for each additional person added to the household, Charges are expected to increase by $404.13, when the Annual Income is held constant. This model produces the following statistical evidence:

Model Summary of using Household to predict Charges

R RІ Adjusted RІ Std Error of Estimate

.753 .567 0.558 620.793

Paying particular attention to the RІ values (Table 2), this prediction equation can account for about 55.8% of the variations present within the data. This equation appears to have a stronger fit for predicting credit card charges then using Income.

To construct a better prediction equation that produces a stronger linear relationship with the least amount of unexplained variance, a multiple regression analysis was conducted. Results of this analysis clearly indicate that using both Income and Household together to predict credit card charges is a better fit then just one of these characteristics. A multiple regression analysis produces a model prediction equation of Annual Charges = 33.13(Income) + 356.30(Household) + 1304.91. To determine how well this equation model fits, a multiple linear regression model containing the two characteristics variables was fitted to the data. The model assumptions were checked using a full residual analysis. The residual plots are shown in Exhibit 2.

The two plots indicate clear relationships between the Amount Charged and each of the explanatory variables. The relationships seem to be more-or-less straight-line, although there is some indication of possible outliers in the plot against income as some points appears to deviate from the trend of the rest of the points within the