Case Study Consumer Research Inc.

This case study included information on a sample of fifty credit card accounts. This information, table one, included household size, annual income, and the amount charged to the account. Scatter plots of the data were produced. Figure one shows household size vs. amount charged. This graph shows that the positive linear relationship of the data is somewhat strong. The r squared is 0.56, analyzing the graph there is a correlation of household size to amount charged, but there is a range per household size.

Figure two shows annual income vs. amount charged. The linear relationship of the data is weak, with an r squared of 0.398. Though a positive linear relationship is present.

The last scatter plot, Figure 3, shows household size vs. annual income. This graph shows that there is no correlation at all between these two factors. Making the factors independent of each other and viable for use in multiple regression.

Frequency tables and plots of annual incomes and household size from the sample were also constructed. Figure four plots the frequency of household size. From this plot we can see that a household size of 2 is most common, with 30 percent of the entire sample. Table 2 shows a breakdown of the frequencies.

Figure five is a plot of the frequency of household incomes separated by $5000 steps. We can see that the incomes of the sample are close to evenly distributed with peaks at 30-34 and 50-54. Table three shows the frequencies and percents of household incomes from the sample.

Regressions of the data were also performed. First a regression with the annual income as the independent variable and the amount charged dependent

. With this regression an estimated regression equation is formed, Y=2203.999 + 40.479(income). This equation shows that there is a positive relationship between the amount charged and annual income. The p value is very low, 0.0000009012, well under the significance alpha of 0.05, and F. This means that the relationship is significant, and a larger the annual income mean the amount charged is higher.

The Second regression was performed with household size as he independent variable. The regression equation produced by this is 2581.94 + 404.12 (household size). This equation shows a positive linear relationship between household size and amount charged to the card. The p value obtained from the regression is 0.0000000002864. This value is also well under the significance alpha of 0.05. This means that there is a strong relationship between household size and amount charged. The larger the household size the larger the amount charged grows.

A multiple regression was also performed on the data. This regression held the amount charged dependent

and the household size and annual income independent. A regression equation was also obtained, Y = 1304.90 + 356.26 (household size) + 33.13 (Annual income). This means that there is a positive linear relationship between these three variables. This also means that household size has a greater effect on amount charged than annual income. The p value for this regression is 3.124E-14, and 7.68E-11 for household size and annual income respectively. These values are well below the significance alpha of 0.05. This means that the data is relevant and there is a significant relation ship between household size, annual income, and amount charged. The r squared from this regression is 0.8255 meaning that with both of these variables the regression equation is much more linear