The asking price of a home is influenced by many different factors such as the number of bedrooms, number of bathrooms, square footage, and the lot size. A random sample of 13 recent home sales collected including the aforementioned variables is given in Table 8.8.

a. Write the population linear regression equation.

b. Using this data set, develop a model that can be used to predict the asking price of a home based on the number of bedrooms, number of bathrooms, square footage, and the lot size.

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

d. Is the overall model useful in predicting the asking price?

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

f. What factors are significant in predicting the asking price? 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 asking price would be for a home with four bedrooms, three bathrooms, which is 3,500 square feet and is on 1.25 acres.
h. Can you think of any other factors that could impact the asking price of a home?

Table 8.8

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Asking Price (in Thousands of Dollars), Number of Bedrooms, Number of Bathrooms, Square Footage (in Feet), and Lot Size (in Acres) for a Random Sample of 13 Recent Home Sales Observation Asking Price (in Dollars) Number of Bedrooms Number of Bathrooms Square Footage (in Feet) Lot Size (in Acres) 1 209 5 13 77 57 2 226 9 15 142 52 3 224 4 275 5698 334 155 378 0 12 51 27 16 108 41 19 127 51 6 8 100 48 7 184 266 12 12 5 11 81 38 16 189 44 9 303 16 19 251 17 10 228 3 12 49 60 11 275 4 16 68 53 12 13 23 291 332 27 19 191 23 20 112 64