Consumer Research Stats Case Analysis

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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…show more content…
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 R² Adjusted R² Std Error of Estimate
.753 .567 0.558 620.793

Paying particular attention to the R² 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

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