The data in Table 8.6 gives the amount of credit card debt for a sample of 24 individuals along with their age, education level, and yearly salary.

a. Write the population linear regression equation.

b. Using this data set, develop a model that can be used to predict credit card debt based on age, education, and salary.

c. Is the overall model useful in predicting credit card debt?

d. Draw a matrix plot that shows the relationship between the response and each of the predictor variables.

e. Use exploratory techniques and any formal tests to check relevant model assumptions and check for multicollinearity.

f. What factors are significant in predicting credit card debt? Interpret your findings in the context of the problem, and comment on whether you think your conclusions make sense.

g. Using your estimated regression equation, estimate what the average credit card debt would be for an individual who is 25 years old, with 20 years of education, and whose salary is \(\$ 50,000\) per year.

h. Can you think of any other factors that could influence the amount of credit card debt?

Table 8.6

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Credit Card Debt, Age, Education, and Yearly Salary Credit Card Debt Observation (in Dollars) Age (in Years) Education Level (in Years) Yearly Salary (in Thousands of Dollars) 123 5,020 45 16 55 8,550 50 19 75 3 6,750 48 18 68 4 1,255 29 18 42 5698 0 19 12 25 0 20 13 38 7 4,685 35 16 50 5,790 33 14 57 9 2,150 30 16 42 10 550 19 12 35 11 6,850 22 16 42 12 1,250 45 16 58 13 460 50 16 62 14 1,280 35 12 39 15 500 28 14 52 16 430 32 14 58 17 250 44 12 35 18 650 49 19 1,285 32 20 690 50 21 500 18 22 6,000 30 23 7,500 39 24 12,850 32 2122 12 41 14 57 12 35 13 41 17 90 16. 54 20 85