Suppose that you are commissioned to develop a forecasting model for residential property selling price in a suburb. The sample information available to you is collected from 270 homes recently sold in this suburb.

Key-

SalePrice (Y) : The transaction price in thousand dollars, as recorded on the contract of sale.

LandArea (X1): The area of the land in square metres.

Rooms: (X2) The number of main rooms in a dwelling. Main rooms include bedrooms, living areas, and kitchens, but exclude bathrooms, laundries, and water closets. 2 Groups of small rooms that are not fully enclosed may be counted as one room (e.g. kitchen-dinettes).

EquivArea (X3): Recorded in square metres. This is a weighted average of all buildings on the property. The main dwelling will have a weighting of 1, lesser structures such as carports will have a lower weighting. These weightings are not fixed and depend upon the discretion of the assessor. The overall value is a reasonable proxy for the building area.

Condition (c): This is a subjective condition code with the value 0 indicating some minor structural problems or the need for repairs, the value 1 indicating good condition and the value 2 indicating excellent condition.

Years (X4): The number of years from the year the house was built to the year the house was sold.

1) With the following develop a dummy variable named D for house condition such that it takes the value 1 if the if the original condition variable C taking the values 1 and 2, otherwise takes the value 0. Suppose that you begin with exploring a regression model,

ln (Y) = a + 1 X1 + 2 X2 + 3 X3 + 4 X4 + 5 D + e.

address the regression anaylsis and the estimated model.

2) What are the statistically significant explanatory variables in the model in Question 1 above? Why?

3) After some statistical investigation you may select a regression model

Y = a + 1 X1 + 2 X3 + 3 D * X1 + e

address the regression analysis of the model. Interpret the estimate of 3.

4) a) Predict house price for a house in a very good condition that has 700 square metres for LandArea, 4 main rooms, 200 square metres for EQM, and 10 years for YearsBuilt based on the models in Questions 1 and 3, separately.

b) how confidence are you on the prediction in question 4a) provide reasoning

SalePrice	LandArea	Rooms	EquivArea	Condition	Years
447.5 610 575 420 480 917.5 705 810 450 500 567 625 435 1040 700 526 555 720 521.5 575 480 490 361 840 1200 715 403 575 875 685 620.55 595 655 490 732 542 648 565 868 392 555 565 915 597.5 425 480 405 618 732 673 570 506 720 510 536 625 805 637 855 590 360 520 534.3 615 680 415 489 512.5 490 580 462.5 730 605 560 965 667.5 482.5 705 755 1500 700 375 760 565 870 880 545 419.5 785 710 674 583 1041.6 595 548.5 1020 600 612.5 562.5 405 507 553 565 600 471 551 679 690 595 520 881 1350 805 1410 900 540 450 600 673.5 1250 501 500 670 530 610 460 510 612.5 603 605 706 648 555 750 500 480 669 390 577 1300 500 506 503 565 734 525.5 520 830 550 390 1050 565 561 800 620 705 622 1020 680 765 701 720 350 450 650 270 605 434 580 700 592.5 555 578 485 650 570 580 408 675 755 880 468 543 800 780 487.5 460 490 788.76 715 650 675 1000 605 500 705 490 505 725.5 566 510 627 581 695 575 470 620 610.5 655 800 579 590 781 530 602 660 745 650 710 655 572 710 575 521 415 575 556 860 771 555 1527 797.5 650 492 610 518 558 610 545 650 487.5 655 645 880 545 880 885 645 445 582.5 655 810 410 480 812 620 670 622 637 580 1155 591 1410 768.52 1550 485 745 450 608 1200	345 866 842 713 557 957 804 786 746 707 375 903 814 1089 634 607 590 648 644 771 383 554 390 423 1251 836 613 596 415 745 426 372 351 402 864 199 892 691 840 370 840 310 741 673 323 347 714 708 810 457 1054 452 558 439 632 696 697 580 892 392 614 678 488 776 376 301 778 492 602 603 671 900 626 697 669 498 786 595 516 1858 714 827 636 391 713 976 714 378 906 794 829 700 450 355 604 967 1032 707 746 352 727 296 837 702 765 690 388 357 419 658 1207 780 989 1128 766 356 344 669 733 841 660 772 741 546 418 621 737 567 389 725 792 370 340 603 689 364 375 351 644 698 754 801 492 694 725 553 728 450 549 390 1456 530 700 351 631 581 382 663 371 404 753 758 423 345 468 737 778 642 411 711 766 575 700 767 353 330 928 804 687 710 692 383 352 305 762 396 700 697 495 427 468 698 968 629 801 711 615 713 1045 689 354 660 585 795 873 631 418 784 763 399 343 702 857 530 560 477 375 671 766 774 637 592 543 335 402 649 723 505 863 755 488 427 596 870 415 961 698 722 357 866 784 584 660 433 778 566 320 596 495 753 808 749 256 860 869 697 824 729 770 348 976 738 1003 699 1003 670 802 300 585 2480	5 6 6 4 6 6 6 6 6 5 7 5 5 8 9 6 6 8 5 6 6 6 4 8 9 7 6 5 7 5 7 6 7 6 7 5 5 5 9 4 6 5 5 6 5 5 5 6 6 6 5 5 8 5 5 6 9 6 6 5 5 5 5 6 5 4 6 5 5 5 5 6 5 5 10 5 4 7 7 10 5 5 7 5 7 6 6 5 8 7 6 5 10 5 6 9 6 5 6 4 5 6 5 6 5 4 7 7 6 5 7 8 8 8 10 5 5 6 6 9 6 5 7 6 5 5 4 8 7 5 6 4 7 5 6 4 7 4 5 7 5 5 5 5 6 5 6 7 5 5 6 5 6 7 6 6 5 7 6 5 6 5 4 5 5 8 5 5 5 7 5 5 5 4 6 6 4 4 5 5 7 6 5 6 8 5 5 4 7 6 5 6 5 5 4 7 7 5 8 6 5 5 5 9 6 7 5 5 6 6 6 5 7 6 7 4 6 5 5 6 7 7 5 4 6 5 5 5 6 5 7 7 5 5 5 6 6 5 5 5 6 6 6 6 5 9 7 5 5 6 5 3 5 5 8 6 5 5 7 5 6 7 10 6 7 5 8 4 4 8	123 140 130 97 126 199 127 240 95 96 194 121 108 318 267 138 138 220 119 152 167 195 110 300 300 193 150 156 268 135 194 220 231 145 152 146 119 130 350 92 125 155 300 170 114 112 125 120 164 163 128 100 307 142 104 164 225 220 127 150 100 103 162 210 160 113 141 114 160 97 128 154 125 145 335 155 89 203 301 236 120 112 168 199 224 144 131 134 219 162 160 155 412 160 164 290 104 96 95 93 107 174 113 145 122 67 192 186 144 105 162 385 263 217 323 152 95 153 145 407 130 101 139 130 160 132 113 220 194 133 169 200 180 111 95 120 280 110 110 386 113 117 160 112 135 134 121 310 142 92 194 162 151 255 140 148 152 311 178 252 116 107 106 123 194 195 118 125 145 186 105 105 116 117 192 174 122 78 137 140 138 167 145 238 239 95 95 105 301 206 173 166 130 156 113 167 175 133 190 115 132 155 103 204 103 170 160 159 135 188 178 115 175 136 190 189 270 144 152 140 191 190 98 161 112 108 114 200 168 123 427 290 156 93 170 129 127 132 152 159 148 190 130 260 130 295 300 137 100 105 136 186 111 98 204 180 189 124 142 180 144 153 291 138 380 93 256 135 140 220	0 1 0 1 0 1 0 1 0 0 1 0 0 1 1 1 1 2 0 1 1 1 0 1 1 1 0 0 1 0 1 1 1 1 1 1 0 1 2 0 0 1 1 1 0 1 0 0 0 1 1 0 1 0 1 1 1 1 0 1 1 0 1 1 1 1 1 0 0 1 1 0 0 0 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