This is a problem in model selection. A "big box" home improvement store has collected data on its sales and demographic variables relating to its various stores. The cross-sectional data set for these variables is below:

where:

Sales = average monthly store sales (in thousands of dollars) XI = Households in a 5-mile ring that are do-it-youselfers (in thousands) X2 = Average monthly advertising expenditures (in dollars) X3 = Square footage of competitor stores in a 5-mile ring (in thousands) X4 = Households in a 5-mile ring that are below the poverty level (in hundreds] X5 = Weighted average daily traffic count at store intersection

a. Begin by estimating a model with independent variables XI, X2, and X3. Comment on the appropriateness of this model and its accuracy.

b. Now add X4 to the model above and again comment on the appropriateness of the model. Has the accuracy improved?

c. Finally, add X5 to the model and again comment on the accuracy of the model. Use the appropriate summary statistics of the three models to suggest which of the five independent variables should be in the model. Advise the "big box" retailer on which characteristics are important when choosing new store locations.

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Sales 281 269 267 231 265 260 310 324 222 283 241 333 231 239 281 276 299 272 X1 878 887 1,174 957 987 871 1,042 1,165 745 801 946 1,375 842 1,006 1,294 1,002 1,208 943 X2 6,575 6,236 5,665 5,255 5,956 5,976 7,028 7,162 5,201 6,563 5,540 6,936 5,446 5,333 5,824 6,332 6,716 6,348 X3 175 134 88 72 151 82 82 27 99 185 82 129 154 172 94 70 96 152 X4 7.94 7.59 8.88 7.78 7.92 8.19 7.77 8.15 9.01 7.88 9.79 7.93 8.28 7.77 9.06 9.86 7.74 9.66 X5 2,387 3,003 3,079 3,030 3,466 2,563 2,888 3,457 3,004 3,559 2,592 3,379 3,374 3,743 3,249 3,155 2,287 2,803