Essentials Of Business Analytics
1st Edition
ISBN: 9781285187273
Author: Camm, Jeff.
Publisher: Cengage Learning,
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Textbook Question
Chapter 4, Problem 21P
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 customer’s annual household income (x1), number of members of the household (x2), and number of years of post–high 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 customer’s 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 customer’s 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 customer’s 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 customer’s 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 customer’s number of years of post–high 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 customer’s number of years of post–high 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 customer’s 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 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 customer’s 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?
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The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).ŷ = 30 + 0.7x1 + 3x2Also provided are SST = 1200 and SSE = 384.The yearly income of a 24-year-old female individual is _____.
Chapter 4 Solutions
Essentials Of Business Analytics
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- Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?arrow_forwardThe following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.arrow_forward
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