DATA SET"lcavol" "lweight" "age" "lbph" "svi" "lcp" "gleason" "pgg45" "lpsa"-0.5798185 2.7695 50 -1.386294 0 -1.38629 6 0 -0.43078-0.9942523 3.3196 58 -1.386294 0 -1.38629 6 0 -0.16252-0.5108256 2.6912 74 -1.386294 0 -1.38629 7 20 -0.16252-1.2039728 3.2828 58 -1.386294 0 -1.38629 6 0 -0.162520.7514161 3.4324 62 -1.386294 0 -1.38629 6 0 0.37156-1.0498221 3.2288 50 -1.386294 0 -1.38629 6 0 0.765470.7371641 3.4735 64 0.615186 0 -1.38629 6 0 0.765470.6931472 3.5395 58 1.536867 0 -1.38629 6 0 0.85442-0.7765288 3.5395 47 -1.386294 0 -1.38629 6 0 1.047320.2231436 3.2445 63 -1.386294 0 -1.38629 6 0 1.047320.2546422 3.6041 65 -1.386294 0 -1.38629 6 0 1.26695-1.3470736 3.5987 63 1.266948 0 -1.38629 6 0 1.266951.6134299 3.0229 63 -1.386294 0 -0.59784 7 30 1.266951.4770487 2.9982 67 -1.386294 0 -1.38629 7 5 1.348071.2059708 3.442 57 -1.386294 0 -0.43078 7 5 1.398721.5411591 3.0611 66 -1.386294 0 -1.38629 6 0 1.44692-0.4155154 3.516 70 1.244155 0 -0.59784 7 30 1.470182.2884862 3.6494 66 -1.386294 0 0.37156 6 0 1.4929-0.5621189 3.2677 41 -1.386294 0 -1.38629 6 0 1.558140.1823216 3.8254 70 1.658228 0 -1.38629 6 0 1.599391.1474025 3.4194 59 -1.386294 0 -1.38629 6 0 1.6392.0592388 3.501 60 1.474763 0 1.34807 7 20 1.65823-0.5447272 3.3759 59 -0.798508 0 -1.38629 6 0 1.695621.7817091 3.4516 63 0.438255 0 1.17865 7 60 1.71380.3852624 3.6674 69 1.599388 0 -1.38629 6 0 1.731661.446919 3.1246 68 0.300105 0 -1.38629 6 0 1.766440.5128236 3.7197 65 -1.386294 0 -0.79851 7 70 1.80006-0.4004776 3.866 67 1.816452 0 -1.38629 7 20 1.816451.0402767 3.129 67 0.223144 0 0.04879 7 80 1.848452.4096442 3.3759 65 -1.386294 0 1.61939 6 0 1.894620.2851789 4.0902 65 1.962908 0 -0.79851 6 0 1.924250.1823216 6.1076 65 1.704748 0 -1.38629 6 0 2.008211.2753628 3.0374 71 1.266948 0 -1.38629 6 0 2.008210.0099503 3.2677 54 -1.386294 0 -1.38629 6 0 2.02155-0.0100503 3.2169 63 -1.386294 0 -0.79851 6 0 2.047691.3083328 4.1198 64 2.171337 0 -1.38629 7 5 2.085671.4231083 3.6571 73 -0.579818 0 1.65823 8 15 2.157560.4574248 2.3749 64 -1.386294 0 -1.38629 7 15 2.191652.6609586 4.0851 68 1.373716 1 1.83258 7 35 2.213750.7975072 3.0131 56 0.936093 0 -0.16252 7 5 2.277270.6205765 3.142 60 -1.386294 0 -1.38629 9 80 2.297571.442202 3.6826 68 -1.386294 0 -1.38629 7 10 2.307570.5822156 3.866 62 1.713798 0 -0.43078 6 0 2.327281.7715568 3.8969 61 -1.386294 0 0.81093 7 6 2.374911.4861397 3.4095 66 1.7492 0 -0.43078 7 20 2.521721.6639261 3.3928 61 0.615186 0 -1.38629 7 15 2.553342.7278528 3.9954 79 1.879465 1 2.65676 9 100 2.568791.1631508 4.0351 68 1.713798 0 -0.43078 7 40 2.568791.7457155 3.498 43 -1.386294 0 -1.38629 6 0 2.591521.2208299 3.5681 70 1.373716 0 -0.79851 6 0 2.591521.0919233 3.9936 68 -1.386294 0 -1.38629 7 50 2.656761.660131 4.2348 64 2.073172 0 -1.38629 6 0 2.677590.5128236 3.6336 64 1.492904 0 0.04879 7 70 2.684442.1270405 4.1215 68 1.766442 0 1.44692 7 40 2.691243.1535904 3.516 59 -1.386294 0 -1.38629 7 5 2.704711.2669476 4.2801 66 2.122262 0 -1.38629 7 15 2.7180.9745596 2.8651 47 -1.386294 0 0.50078 7 4 2.788090.463734 3.7647 49 1.423108 0 -1.38629 6 0 2.794230.5423243 4.1782 70 0.438255 0 -1.38629 7 20 2.806391.0612565 3.8512 61 1.294727 0 -1.38629 7 40 2.812410.4574248 4.5245 73 2.326302 0 -1.38629 6 0 2.8421.9974177 3.7197 63 1.619388 1 1.90954 7 40 2.853592.7757088 3.5249 72 -1.386294 0 1.55814 9 95 2.853592.0347056 3.917 66 2.008214 1 2.11021 7 60 2.8822.0731719 3.623 64 -1.386294 0 -1.38629 6 0 2.8821.458615 3.8362 61 1.321756 0 -0.43078 7 20 2.887592.0228712 3.8785 68 1.783391 0 1.32176 7 70 2.920472.1983351 4.0509 72 2.307573 0 -0.43078 7 10 2.96269-0.4462871 4.4085 69 -1.386294 0 -1.38629 6 0 2.962691.1939225 4.7804 72 2.326302 0 -0.79851 7 5 2.972981.8640801 3.5932 60 -1.386294 1 1.32176 7 60 3.013081.1600209 3.3411 77 1.7492 0 -1.38629 7 25 3.037351.2149127 3.8254 69 -1.386294 1 0.22314 7 20 3.056361.8389611 3.2367 60 0.438255 1 1.17865 9 90 3.075012.9992262 3.8491 69 -1.386294 1 1.90954 7 20 3.275263.1411305 3.2638 68 -0.051293 1 2.42037 7 50 3.337552.010895 4.4338 72 2.122262 0 0.50078 7 60 3.392832.5376572 4.3548 78 2.326302 0 -1.38629 7 10 3.43562.6483002 3.5821 69 -1.386294 1 2.584 7 70 3.457892.7794402 3.8232 63 -1.386294 0 0.37156 7 50 3.513041.4678743 3.0704 66 0.559616 0 0.22314 7 40 3.516012.5136561 3.4735 57 0.438255 0 2.32728 7 60 3.530762.6130067 3.8888 77 -0.527633 1 0.55962 7 30 3.56532.677591 3.8384 65 1.115142 0 1.7492 9 70 3.570941.5623463 3.7099 60 1.695616 0 0.81093 7 30 3.587683.3028493 3.519 64 -1.386294 1 2.32728 7 60 3.630992.0241931 3.7317 58 1.638997 0 -1.38629 6 0 3.680091.7316555 3.369 62 -1.386294 1 0.3001 7 30 3.712352.8075938 4.7181 65 -1.386294 1 2.46385 7 60 3.984341.5623463 3.6951 76 0.936093 1 0.81093 7 75 3.99363.246491 4.1018 68 -1.386294 0 -1.38629 6 0 4.029812.5329028 3.6776 61 1.348073 1 -1.38629 7 15 4.129552.8302678 3.8764 68 -1.386294 1 1.32176 7 60 4.385153.8210036 3.8969 44 -1.386294 1 2.16905 7 40 4.684442.9074474 3.3962 52 -1.386294 1 2.46385 7 10 5.143122.8825636 3.7739 68 1.558145 1 1.55814 7 80 5.477513.4719665 3.975 68 0.438255 1 2.90417 7 20 5.58293

Please answer all questions and show your steps clearly. Round off your numerical answers to 4 significant figures. You may use SAS and/or R to do calculations. Please include the program codes in your answer script.

Question 1. Is there structural break in the price level data?

It is suggested that there is a structural break in the price level. The period before 2007 is one regime. The period 2007 and after is another. Consider the model

CP I = ?0 + ?1(Y ear) + ?2D + ?3(D)(Y ear).

where D is a dummy variable: 0 for before the break and 1 for after. We want to test the if the so-called structural break is significant. We have the following computer output:

Full model d. f. SS MS F Sig. Regression 3 3047 .5 1015. 833333 4353. 571429 2. 11752E-10 Residual 6 1.4 0. 233333333 Total 9 3048.9 Reduced model d. f. SS MS F Sig. Regression 1 3012. 148485 3012. 148485 655 . 6787599 5. 80084E-09 Residual 8 36. 75151515 4. 593939394 Total 9 3048.9