What factors influence how much people are willing to spend on a mortgage or rent payment? The data set in Table 8.9 consists of a random sample of 20 residences and it contains measures of the monthly rent/mortgage payment, total household income, monthly utilities, the number in the household, total commute time, the number of vehicles, and the number of workers.

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

b. Use this data set to develop a linear model that can be used to predict which factors, if any, impact the amount spent on mortgage or rent payments \((\alpha=0.10)\).

c. Using exploratory plots and formal tests, check the regression model assumptions and comment on whether you believe these model assumptions appear to hold true.

d. Is the overall model useful in predicting the amount spent on mortgage or rent payments?

e. What variables impact the amount spent on mortgage or rent payments?

Table 8.9

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Monthly Rent/Mortgage Payment, Total Household Income, Monthly Utilities, Number in the Household, Total Commute Time, Number of Vehicles, and Number of Workers Rent/Mortgage Monthly Income Monthly Utilities Number in Total Commute Number of Number of (in Dollars) Household Time (in Minutes) Vehicles (in Dollars) 290 82 Workers 2 2 1 112031 1 1 1 0 2 (in Dollars) 1,845 5,593 4 1,870 2,959 139 1 1,160 2,859 187 31 950 894 2,000 1,444 175 119 4 0 800 125 2,640 3,470 277 1,250 959 135 1,650 2,584 199 3,450 3,865 459 5,980 13,057 561 2,765 3,358 338 3,430 5,337 401 2,080 2,902 288 1,360 2,778 220 1,860 2,896 172 1,160 4,113 345 1,070 4,821 376 3,980 6,851 222 4 2 2 322 3 1848 18 12131 25 30 15 4 50 35 25 35 30 45 45 30 1,280 786 110 2 21102021131 113. 1 2 2 35 2