Chapter 7, Problem 4DTM

Consider again the example introduced in Section 7.5 of a credit card company that has a database of information provided by its customers when they apply for credit cards. An analyst has created a multiple regression model for which the dependent variable in the model is credit card charges accrued by a customer in the data set over the past year (y), and the independent variables are the customers annual household income (x1), number of members of the household (x2), and number of years of post-high school education (x3). Figure 7.23 provides Excel output for a multiple regression model estimated using a data set the company created. a. Estimate the corresponding simple linear regression with the customers annual household income as the independent variable and credit card charges accrued by a customer over the past year as the dependent variable. Interpret the estimated relationship between the customers annual household income and credit card charges accrued over the past year. How much variation in credit card charges accrued by a customer over the past year is explained by this simple linear regression model? b. Estimate the corresponding simple linear regression with the number of members in the customers household as the independent variable and credit card charges accrued by a customer over the past year as the dependent variable. Interpret the estimated relationship between the number of members in the customers household and credit card charges accrued over the past year. How much variation in credit card charges accrued by a customer over the past year is explained by this simple linear regression model? c. Estimate the corresponding simple linear regression with the customers number of years of posthigh school education as the independent variable and credit card charges accrued by a customer over the past year as the dependent variable. Interpret the estimated relationship between the customers number of years of posthigh school education and credit card charges accrued over the past year. How much variation in credit card charges accrued by a customer over the past year is explained by this simple linear regression model? d. Recall the multiple regression in Figure 7.23 with credit card charges accrued by a customer over the past year as the dependent variable and customers annual household income (x1), number of members of the household (x2), and number of years of post-high school education (x3) as the independent variables. Do the estimated slopes differ substantially from the corresponding slopes that were estimated using simple linear regression in parts (a), (b), and (c)? What does this tell you about multicollinearity in the multiple regression model in Figure 7.23? e. Add the coefficients of determination for the simple linear regression in parts (a), (b), and (c), and compare the result to the coefficient of determination for the multiple regression model in Figure 7.23. What does this tell you about multicollinearity in the multiple regression model in Figure 7.23? f. Add age, a dummy variable for sex, and a dummy variable for whether a customer has exceeded his or her credit limit in the past 12 months as independent variables to the multiple regression model in Figure 7.23. Code the dummy variable for sex as 1 if the customer is female and 0 if male, and code the dummy variable for whether a customer has exceeded his or her credit limit in the past 12 months as 1 if the customer has exceeded his or her credit limit in the past 12 months and 0 otherwise. Do these variables substantially improve the fit of your model?

Consider again the example introduced in Section 4.5 of a credit card company that has a database of information provided by its customers when the customers apply for credit cards. An analyst has created a multiple regression model for which the dependent variable in the model is credit card charges accrued by a customer in the data set over the past year (y), and the independent variables are the customers annual household income (x1), number of members of the household (x2), and number of years of posthigh school education (x3). Figure 4.23 provides Excel output for a multiple regression model estimated using a data set the company created. a. Estimate the corresponding simple linear regression with the customers annual household income as the independent variable and credit card charges accrued by a customer over the past year as the dependent variable. Interpret the estimated relationship between the customers annual household income and credit card charges accrued over the past year. How much variation in credit card charges accrued by a customer over the past year does this simple linear regression model explain? b. Estimate the corresponding simple linear regression with the number of members in the customers household as the independent variable and credit card charges accrued by a customer over the past year as the dependent variable. Interpret the estimated relationship between the number of members in the customers household and credit card charges accrued over the past year. How much variation in credit card charges accrued by a customer over the past year does this simple linear regression model explain? c. Estimate the corresponding simple linear regression with the customers number of years of posthigh school education as the independent variable and credit card charges accrued by a customer over the past year as the dependent variable. Interpret the estimated relationship between the customers number of years of posthigh school education and credit card charges accrued over the past year. How much variation in credit card charges accrued by a customer over the past year does this simple linear regression model explain? d. Recall the multiple regression in Figure 4.23 with credit card charges accrued by a customer over the past year as the dependent variable and customers annual household income (x1), number of members of the household (x2), and number of years of posthigh school education (x3) as the independent variables. Do the estimated slopes differ substantially from the corresponding slopes that were estimated using simple linear regression in parts a, b, and c? What does this tell you about multicollinearity in the multiple regression model in Figure 4.23? e. Add the coefficients of determination for the simple linear regression in parts a, b, and c, and compare the result to the coefficient of determination for the multiple regression model in Figure 4.23. What does this tell you about multicollinearity in the multiple regression model in Figure 4.23? f. Add age, a dummy variable for gender, and a dummy variable for whether a customer has exceeded his or her credit limit in the past 12 months as independent variables to the multiple regression model in Figure 4.23. Code the dummy variable for gender as 1 if the customers gender is female and 0 if male, and code the dummy variable for whether a customer has exceeded his or her credit limit in the past 12 months as 1 if the customer has exceeded his or her credit limit in the past 12 months and 0 otherwise. Do these variables substantially improve the fit of your model?

On May 1, the billing date, Kayla had a balance due of $673.64 on her credit card. In May, Kayla made a purchase of$264.03 on May 6, made a payment of$100 on May 22, and made another payment of$300 on May 28. Determine her finance charge on June 1 using the previous balance method. Assume that the interest rate is 3.15% per month. Then determine Kayla’s new balance on June 1.