The data presented below are for retail sales in the United States quarterly from the period 1992Q1 through 2003Q4. Also included is disposable personal income per capita (DPIPC) (to use as a measure of the well-being of the economy).

a. Develop a regression model of retail sales as a function of the S&P 500. Comment on the relevant summary statistics.
b. Estimate a new multiple-regression model using seasonal dummy variables for quarters 2, 3, and 4. Additionally, add a time index to account for trend. Comment on the relevant statistics of this model. Is this model an improvement on the model above? What evidence is there that this second model provides an improvement (no improvement)','
c. Square the time index variable and add it to the multiple-regression model above. Does the resulting model perform better than either previous model? Explain your reasoning.

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RS DPIPCQ2Q3Q4T T2 DPIPC"2 534,392 20,763 0 4 441,378,081 9 449,567,209 16 457,318,225 25 467,900,161 36 474,673,369 Sep-97 623,555 22,023 0 1 07 49485,012,529 64 498,048,489 81 517,699,009 655,691 23,060 0 0 10 100 531,763,600 Sep-98 644,369 23,315 0 0 11 121 543,589,225 Dec-98 706,267 23,511 00 12 144 552,767,121 0 13 169 560,931,856 702,714 23,806 100 14 196 566,725,636 Sep-99709,527 23,979 0 0 15 225 574,992,441 116 256 595,311,201 Mar-00 696,048 25,094 0 0 17 289 629,708,836 Jun-00 753,211 25,321 1 0 0 18 324 641,153,041 Sep-00 746,875 25,690 0 0 19 361 659,976,100 1 20 400 663,989,824 Mar-01 704,757 25,996 0 0 021 441 675,792,016 79,011 25,985 1o 22 484 675,220,225 Sep-01 756,128 26,665 0 1 0 23 529 711,022,225 Dec-01 827,829 26,250 0 0 24 576 689,062,500 0 25 625 727,704,576 790,486 27,224 1 0 0 26 676 741,146,176 Sep-02 792,657 27,163 0 0 27 729 737,828,569 Dec-02 833,877 27,217001 28 784 740,765,089 Mar-03 741,060 27,480 0 0 0 29 841 755,150,400 819,232 27,800 00 30 900 772,840,000 0 31 961 802,135,684 Dec-03 874,493 28,473 0 0 1 32 1024 810,711,729 Mar-04 794,720 28,922 0 0 33 1089 836,482,084 870,834 29,300100 34 1156 858,490,000 Sep-04 872,340 29,576 0 0 35 1225 874,739,776 595,893 21,009 644,297 21,385 0 17,25221,78700 6 Sep-96 592,083 21,203 0 1 0 3 Mar-97 Dec-97669,032 22,317 580,778 22,753o Mar-99 627,589 23,684 0 768,726 24,399 0 Dec-00 792,622 25,768 0 717,302 26,976 0 Jun-03 Sep-03 830,692 28,322 0 Dec-04 936,446 30,265 00 136 1296 915,970,22 Mar-05 835,280 30,106 0 0 0 37 1369 906,371,236 0 38 1444 928,847,529 Sep-05 939,788 30,622 0 1 0 39 1521 937,706,884 Dec-05 986,849 31,252 0 40 1600 976,687,504 Mar-06 906,635 31,693 0 00 41 1681 1,004,446,249 Jun-06 1,002,064 31,970 00 42 1764 1,022,080,900 Sep-06 993,749 32,231 43 1849 1,038,837,361 Jun-05 931,513 30,477 Dec-06 1,034,094 32,561 0 01 44 1936 1,060,218,72 Mar-07 0 45 2025 1,102,638,436 Jun-07 1,030,508 33,525 1 0 0 46 2116 1,123,925,625 Sep-07 1,017,608 33,940 0 047 2209 1,151,923,600 934,619 33,206 0