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Data for this problem are in the table below. These data enable you to apply the methods that we are studying to the real estate

Data for this problem are in the table below. These data enable you to apply the methods that we are studying to the real estate area to answer this two-part question.

The data set contains information about apartment prices and characteristics for a central area of a city. The data include sale price (PRICE) in $, floor area (SQFT) in square feet, number of bedrooms (BED), number of bathrooms (BATH), number of floors in the building (FLOORS), and distance from a crowded and busy city landmark, the 'Presidential Tower' (PDIST) in feet.

The type of model that we study in this problem (regressing price against characteristics of dwelling and location) is commonly used for automating property tax assessments.

(a) A realtor tells you the following about the apartments you are interested in,

1.The price of the apartment increases if the apartment is in a building with fewer number of floors. Do you agree with the realtor? Please formulate a test to answer this question.

2. Price of the apartment increases if it is farther from the Presidential Tower. Do you agree with the realtor? Please formulate a test to answer this question.

3. You are looking at apartments in a particular area which is some distance away from the Presidential Tower. Also, you are looking for apartments in buildings that have 12 floors. However, the prices are overshooting your budget. The realtor tells you that to get a lower price for an apartment either you move a mile closer to the Presidential building and look for apartments in buildings with 15 floors or you look at the same place where you are looking but consider similar sized apartments (with same bedrooms and bathrooms) in buildings which have 16 floors. The realtor claims that the reduction in price would be the same in both cases.

Do you agree with the realtor? Please formulate a test to answer this question.

PRICE SQFT BED BATH FLOORS PDIST
255000 518 0 1 9 8000
300000 514 0 1 14 420
395000 471 0 1 4 1600
340000 520 0 1 4 8000
230000 297 0 1 3 7520
1250000 668 0 1 3 3340
235000 427 0 1 15 420
305000 508 0 1 13 420
460000 450 0 1 3 10020
310000 368 0 1 3 7740
235000 327 0 1 3 7740
180000 330 0 1 3 7740
190000 345 0 1 3 7740
310000 372 0 1 3 7740
325000 583 0 1 10 8000
365000 675 0 1 8 9660
270000 305 0 1 3 1700
325000 520 0 1 4 8000
255000 298 0 1 3 160
400000 608 0 1 11 8000
265000 422 0 1 4 2460
380000 436 0 1 8 3200
140000 330 0 1 16 420
405000 505 0 1 4 6340
315000 535 0 1 15 420
265000 514 0 1 16 420
155000 290 0 1 16 420
230000 267 0 1 9 7240
640000 1188 0 2 4 9140
320000 514 0 1 15 420
175000 258 0 1 4 5220
390000 492 0 1 16 6600
210000 362 0 1 6 5860
380000 530 0 1 4 1160
210000 262 0 1 16 420
290000 458 0 1 5 1840
400000 433 0 1 5 1640
145000 216 0 1 8 7240
425000 520 0 1 10 8000
160000 330 0 1 5 1120
275000 418 0 1 4 1700
190000 258 0 1 4 5220
425000 590 0 1 10 8000
425000 548 0 1 10 8000
145000 262 0 1 16 420
240000 427 0 1 15 420
175000 290 0 1 15 420
320000 535 0 1 14 420
455000 596 0 1 10 3200
380000 500 0 1 4 1160
455000 553 0 1 4 4080
315000 514 0 1 15 420
312500 514 0 1 14 420
170000 330 0 1 16 420
205000 340 0 1 5 1120
420000 476 0 1 4 5220
310000 340 0 1 5 1120
365000 461 0 1 4 9240
465000 582 0 1 5 6340
400000 673 0 1 11 8000
215000 340 0 1 5 1120
700000 764 1 1 3 7420
1075000 1145 1 2 4 5160
905000 1322 1 1 4 4580
320000 564 1 1 4 9560
310000 636 1 1 6 10400
575500 542 1 1 7 5560
260000 438 1 1 15 420
725000 912 1 1 4 5460
420000 560 1 1 4 4640
350000 560 1 1 4 7880
410000 675 1 1 4 7020
490000 790 1 1 4 7260
415000 735 1 1 5 5860
642500 670 1 1 7 5480
305000 427 1 1 15 420
400000 561 1 1 4 7420
829000 1010 1 1 4 2360
350000 524 1 1 4 7420
450000 574 1 1 4 2460
705000 860 1 2 4 7000
265000 563 1 1 4 3340
320000 574 1 1 13 420
340000 590 1 1 6 6720
505000 870 1 1 4 5040
712500 711 1 1 4 5160
575000 750 1 1 8 5600
385000 581 1 1 8 7240
425000 718 1 1 12 8000
220000 426 1 1 16 420
275000 429 1 1 3 10400
507500 583 1 1 4 9240
897500 791 1 1 3 7120
610000 715 1 1 4 2060
340000 355 1 1 4 7420
575000 662 1 1 4 5500
375000 588 1 1 13 420
200000 350 1 1 13 9660
625000 963 1 1 4 3800
225000 500 1 1 4 6840
602500 632 1 1 4 9240
780000 1100 1 2 5 2720
700000 635 1 1 4 9240
425000 494 1 1 4 4800
365000 515 1 1 3 6840
200000 407 1 1 6 10400
385000 577 1 1 5 9760
210000 426 1 1 16 420
425000 562 1 1 4 1280
605000 1072 1 1 16 3200
315000 563 1 1 15 420
330000 697 1 1 4 9560
850000 768 1 1 10 9800
395000 621 1 1 4 7920
500000 721 1 1 4 5500
395000 581 1 1 8 7240
460000 545 1 1 4 7080
395000 725 1 1 4 10020
660000 943 1 2 4 2580
465000 625 1 1 4 7080
155000 325 1 1 16 420
360000 600 1 1 14 420
490000 623 1 1 4 5580
670000 1008 1 1 4 4120
559205 642 1 1 7 5640
530000 1041 1 2 16 8000
355000 590 1 1 4 6400
370000 694 1 1 4 2640
395000 745 1 1 4 10020
765000 870 1 1 11 9800
880000 870 1 1 11 9800
592500 857 1 1 4 9140
238000 690 1 1 9 9620
875000 870 1 1 11 9800
575000 586 1 1 4 2920
550000 663 1 1 11 8000
550000 663 1 1 11 8000
440000 656 1 1 4 5160
400000 748 1 1 4 2640
425000 673 1 1 11 8000
1135000 1405 1 1 4 3560
470000 790 1 1 13 8000
325000 529 1 1 4 4800
635000 676 1 1 11 8000
410000 556 1 1 4 5300
505000 681 1 1 12 3200
555000 583 1 1 4 9240
450000 586 1 1 12 9280
475000 725 1 1 12 9280
675000 1041 1 2 16 8000
415000 735 1 1 5 5860
210000 427 1 1 16 420
450000 718 1 1 12 8000
625000 745 1 1 12 8000
445000 785 1 1 4 2640
465000 745 1 1 12 8000
435000 639 1 1 4 2700
620000 575 1 1 4 8100
400000 729 1 1 4 2640
400000 663 1 1 4 2640
415000 742 1 1 4 2640
600000 767 1 2 13 8000
562500 698 1 1 4 5540
630000 767 1 2 13 8000
320000 490 1 1 4 6840
622500 616 1 1 4 9240
525000 767 1 2 13 8000
740000 730 1 1 4 2060
475000 772 1 1 13 8000
490000 1041 1 2 16 8000
460000 600 1 1 4 9240
345000 459 1 1 13 420
285000 500 1 1 4 6840
612500 730 1 1 4 5440
350000 784 1 1 13 8000
490000 784 1 1 13 8000
430000 685 1 1 5 4840
335000 591 1 1 13 420
375000 640 1 1 4 8100
385000 588 1 1 13 420
325000 529 1 1 4 7880
265000 459 1 1 13 420
345000 560 1 1 4 7420
390000 574 1 1 13 420
325000 475 1 1 10 9660
470000 750 1 1 4 4680
925000 1004 1 1 16 6600
325000 602 1 1 4 7760
605000 626 1 1 4 6300
400000 582 1 1 4 7420
346900 591 1 1 14 420
600000 638 1 1 4 7960
775000 913 1 1 4 4840
565000 714 1 1 7 5600
668750 770 1 1 4 3560
285000 438 1 1 14 420
375000 574 1 1 12 420
643200 663 1 1 4 3340
335000 425 1 1 4 5440
625000 622 1 1 4 3480
375000 657 1 1 4 6920
675000 722 1 1 4 6260
261250 438 1 1 14 420
750000 1002 1 1 4 600
780000 752 1 1 4 9240
400000 833 1 2 5 2740
265000 438 1 1 15 420
240000 804 1 1 5 3260
325000 563 1 1 16 420
225000 409 1 1 15 420
825000 906 1 1 4 5260
310000 514 1 1 15 420
435000 720 1 1 4 2640
668750 750 1 1 8 3560
460000 675 1 1 4 7020
750000 950 1 1 4 5720
425000 666 1 1 8 3760
150000 325 1 1 15 420
425000 485 1 1 8 9660
380000 588 1 1 13 420
952500 1866 1 1 4 4280
445000 670 1 1 4 8140
240000 350 1 1 12 9660
385000 628 1 1 11 9280
460000 965 1 1 4 2980
625000 555 1 1 4 1720
450000 562 1 1 4 9720
515000 798 1 1 4 6500
261250 426 1 1 16 420
445000 745 1 1 12 8000
415000 559 1 1 8 7240
515000 589 1 1 5 5580
580000 676 1 1 11 8000
400000 585 1 1 6 5900
405000 609 1 1 6 4880
395000 692 1 1 8 7240
715000 633 1 1 4 5500
590000 670 1 1 6 6760
775000 730 1 1 5 6680
335000 567 1 1 5 5580
325000 722 1 1 5 8420
733000 903 1 2 6 6300
465000 627 1 1 5 9720
375000 560 1 1 13 420
887500 1004 1 1 16 6600
340000 563 1 1 16 420
130000 325 1 1 16 420
625000 586 1 1 4 3280
775000 930 1 2 5 2720
485000 676 1 1 11 8000
700000 742 1 1 5 1640
639500 898 1 1 5 9720
750000 1035 1 2 16 8000
625000 689 1 1 5 6680
360000 450 1 1 11 420
565000 730 1 1 5 6680
400000 578 1 1 7 3720
575000 658 1 1 5 6300
1000000 1324 1 2 6 5200
985000 870 1 1 10 9800
612500 721 1 1 4 5500
455000 743 1 1 5 1840
525000 1035 1 2 16 8000
540000 727 1 1 5 2660
600000 708 1 1 4 4920
392500 522 1 1 4 1160
225000 409 1 1 15 420
937500 1169 1 2 16 8000
395000 528 1 1 4 1160
430000 767 1 2 13 8000
550000 1472 1 1 16 3200
485000 772 1 1 13 8000
315000 690 1 1 9 9620
470000 668 1 1 5 6300
455000 611 1 1 4 4140
555000 663 1 1 11 8000
692500 645 1 1 7 5600
550000 676 1 1 11 8000
665000 686 1 1 5 6680
349200 588 1 1 14 420
675000 1846 1 2 4 7960
475000 666 1 1 8 3760
550000 605 1 1 5 6760
410000 627 1 1 8 7240
713970 659 1 1 7 5600
320000 563 1 1 16 420
350000 574 1 1 4 2460
435000 860 1 1 6 5860
475000 703 1 1 6 100
320000 459 1 1 13 420
275000 438 1 1 14 420
580000 745 1 1 12 8000
660000 645 1 1 7 5600
930000 870 1 1 10 9800
410000 574 1 1 12 420
425000 755 1 1 12 8000
360000 784 1 1 13 8000
350000 588 1 1 13 420
375000 673 1 1 11 8000
300000 438 1 1 14 420
675000 767 1 2 13 8000
850000 968 1 1 7 100
440000 607 1 1 4 8740
425000 701 1 1 8 7240
310000 563 1 1 16 420
600000 657 1 1 4 6260
450000 670 1 1 4 8140
575000 1041 1 2 16 8000
727500 606 1 1 6 5600
287500 438 1 1 14 420
365000 622 1 1 7 3800
310000 459 1 1 13 420
265000 475 1 1 9 9660
1000000 1184 1 2 16 3200
950000 870 1 1 11 9800
320000 427 1 1 16 420
945000 1000 2 2 4 1680
642500 1050 2 2 5 6220
1025000 1292 2 2 4 3460
1550000 1360 2 2 3 2000
847500 1131 2 2 4 560
650000 1121 2 2 6 7640
1025000 1451 2 3 16 8000
710000 805 2 1 5 2700
790000 1339 2 2 4 6360
775000 1121 2 2 6 7640
1150000 1680 2 2 4 2420
640000 713 2 1 3 8600
1975000 1710 2 3 3 1460
1025000 1300 2 2 4 6660
1175000 934 2 1 4 4920
1085000 1464 2 3 16 8000
840000 885 2 1 4 7260
782500 893 2 1 4 1620
730000 951 2 2 4 4120
965000 1380 2 1 4 3760
905000 1425 2 2 8 6660
625000 1075 2 2 5 8140
740000 890 2 2 4 3580
675000 925 2 1 4 1620
1275000 1810 2 3 4 7180
395000 568 2 1 7 7240
894500 1235 2 1 4 240
601750 840 2 1 6 5900
750000 1271 2 2 6 7640
440000 783 2 1 5 7460
1325000 2000 2 3 4 2340
965000 1380 2 1 4 3760
978750 1015 2 2 7 5480
850000 963 2 2 4 6260
507500 929 2 2 15 420
742500 886 2 1 4 3100
675000 1121 2 2 6 7640
540000 820 2 1 7 9620
950000 1300 2 2 4 6660
525000 897 2 2 13 420
842500 1190 2 2 8 7640
345000 605 2 1 9 9660
600000 866 2 2 4 9540
1200000 1801 2 2 5 4060
562500 861 2 2 13 420
675000 1271 2 2 6 7640
800000 1200 2 2 4 2340
958750 1487 2 2 4 9040
525000 883 2 1 12 9280
710000 896 2 2 7 10400
800000 1015 2 2 4 6300
590000 910 2 1 4 2980
550000 830 2 2 6 7460
415000 830 2 1 6 7460
175000 775 2 1 7 5000
660000 610 2 1 4 5200
1200000 1339 2 3 8 1400
600000 914 2 1 5 8060
650000 1123 2 2 16 8000
875000 1425 2 2 8 6660
1575000 1523 2 2 4 2180
1300000 1552 2 2 8 6660
886250 1045 2 2 4 5500
775000 926 2 1 5 8060
615000 790 2 1 8 7240
1000000 1431 2 2 16 8000
632500 860 2 2 4 1700
415000 783 2 1 5 7460
600000 831 2 1 13 3200
825000 1115 2 2 4 6380
1375000 1207 2 2 9 9800
850000 1197 2 2 16 8000
710000 934 2 1 5 8060
900000 1193 2 2 16 8000
835000 1190 2 2 4 2300
1150000 1453 2 1 4 440
1400000 1520 2 2 4 6540
875000 1000 2 1 16 3200
760000 989 2 2 5 8060
889195 1292 2 2 4 3460
470000 690 2 1 9 9660
711250 989 2 2 5 8060
1000000 1889 2 3 9 1800
912500 1197 2 2 16 8000
1050000 1093 2 2 5 800
995000 1137 2 1 4 1160
1137500 1053 2 2 4 2180
1165000 1132 2 2 10 9800
667500 1133 2 1 4 2980
825000 899 2 2 4 3640
1000000 1312 2 2 8 5600
675000 1050 2 2 5 6220
1300000 1169 2 2 10 9800
625000 748 2 1 4 4140
645000 1100 2 1 4 3540
1250000 1169 2 2 10 9800
700000 1152 2 2 16 8000
787500 1220 2 2 4 5420
1015000 1132 2 2 11 9800
1395000 1392 2 2 11 9800
1275000 1415 2 2 5 4060
1295000 1392 2 2 11 9800
525000 929 2 2 14 420
520000 812 2 1 4 4560
1243750 1190 2 2 10 9800
812500 1736 2 2 7 1300
950000 1197 2 2 16 8000
925000 1425 2 2 7 6660
1075000 1742 2 2 4 3580
912500 1348 2 2 4 700
615000 1053 2 2 5 5580
800000 935 2 2 4 3640
700000 1214 2 2 4 9040
1050000 1223 2 2 4 2180
775000 1016 2 1 4 820
828250 1175 2 2 4 6660
780000 1245 2 2 16 8000
575000 823 2 1 5 7460
825000 805 2 1 4 7260
525000 783 2 1 5 7460
950000 1193 2 2 16 8000
1041050 1340 2 2 4 380
825000 1133 2 2 4 2180
1463925 1130 2 2 16 680
800000 1133 2 2 4 2180
950000 1280 2 2 4 1140
1212500 1445 2 2 4 3720
1075000 1318 2 2 16 8000
1000000 1156 2 2 4 560
725000 894 2 2 4 3640
600000 875 2 2 6 7640
635000 875 2 1 6 7640
792500 790 2 1 3 5740
1100000 1443 2 2 8 6660
560000 929 2 2 14 420
500000 840 2 1 6 5900
1575000 2394 2 3 16 8000
549500 765 2 1 8 9660
1250000 1766 2 2 4 6320
912500 1193 2 2 16 8000
582500 490 2 1 4 2700
580000 885 2 1 4 7260
820000 1133 2 2 5 6260
675000 1121 2 2 6 7640
965000 1469 2 2 16 3200
303000 508 2 1 13 420
825000 895 2 1 4 5740
585000 875 2 2 6 7640
975000 1304 2 2 4 2440
815000 974 2 2 4 6300
550000 970 2 1 4 8140
1495000 1273 2 2 9 9800
810000 1094 2 2 4 5440
1300000 1300 2 2 4 6660
1000000 1175 2 1 4 3940
750000 1271 2 2 6 7640
1075000 720 2 1 4 9560
750000 1221 2 2 16 8000
1025000 1075 2 2 5 1480
854375 963 2 2 4 6260
715000 1113 2 2 4 2180
1175000 1169 2 2 10 9800
1220000 1132 2 2 10 9800
1900000 1876 2 2 4 6320
938000 1876 2 2 4 6320
900000 1245 2 2 4 2720
815000 1245 2 2 16 8000
611750 1020 2 2 7 3600
389200 977 2 2 4 980
542500 929 2 2 14 420
975000 1530 2 2 4 3760
562500 925 2 1 7 3600
950000 1339 2 3 7 1800
862500 1197 2 2 16 8000
925000 1193 2 2 16 8000
1312500 1095 2 2 4 1480
420050 693 2 1 6 10400
1262500 1442 2 3 4 560
1038500 1073 2 2 16 1900
1500000 1700 2 2 4 3760
475000 929 2 2 15 420
710000 1050 2 2 5 6220
975000 1164 2 2 16 6600
1150000 1536 2 2 8 6660
1490000 1273 2 2 9 9800
1172500 1293 2 2 16 3600
1325000 1293 2 2 16 3600
650000 801 2 1 4 6260
971000 971 2 2 5 1900
1025000 983 2 2 15 8000
1143465 1177 2 3 4 3340
1550000 1430 2 2 4 2140
1650000 2163 2 1 16 1880
1000000 1107 2 2 5 8240
875000 1108 2 2 4 1480
1337500 1754 2 3 16 3200
940000 1315 2 2 16 8000
1810000 1409 2 3 16 3600
930000 1302 2 2 16 8000
662500 1050 2 2 5 6220
1550000 2363 2 3 16 8000
1075000 1293 2 2 16 3600
583500 782 2 1 5 7460
555000 781 2 1 5 2700
1085000 1345 2 2 16 8000
1510000 1273 2 2 9 9800
900000 1263 2 2 16 8000
692500 834 2 2 5 5000
625000 1160 2 2 16 420
2250000 2264 2 2 5 8240
2450000 2220 2 3 16 3600
1715000 2434 2 3 16 8000
1675000 1795 3 2 7 4440
1230000 1973 3 2 8 6660
1950000 2030 3 2 4 6660
2050000 1940 3 3 4 740
800000 1131 3 1 7 5900
1262500 1403 3 1 3 6940
847500 1070 3 2 7 3600
970000 1380 3 1 4 3540
1200000 1940 3 1 6 6160
800000 1889 3 3 4 7120
2075000 1445 3 2 9 9800
1100000 1600 3 2 4 2580
1975000 2450 3 2 5 2720
1450000 2120 3 3 4 2340
1705000 1445 3 2 9 9800
570000 1171 3 2 5 8220
1350000 1940 3 1 6 6160
1500000 2030 3 2 4 6660
1285000 1070 3 2 6 5600
2975000 2146 3 1 12 8240
850000 1500 3 2 4 5720
1930000 1577 3 2 9 9800
1725000 2210 3 2 5 2720
1800000 1815 3 3 6 8240
1825000 1787 3 2 8 1800
1835000 2162 3 3 16 6600
760000 1274 3 2 4 3900
890000 1019 3 1 8 3680
1575000 1892 3 2 4 600
725000 1900 3 3 4 3560
1255000 1563 3 3 5 800
2875000 1735 3 3 5 800
1250000 1395 3 2 3 7120
1085000 2511 3 2 16 420
2125000 2325 3 3 5 3760
1475000 1700 3 2 4 1620
1010000 1747 3 2 7 1300
1065000 1506 3 2 5 8060
1945000 2331 3 3 8 3820
1625000 1389 3 1 4 1920
1375000 2325 3 3 4 2180
1025000 1445 3 2 5 800
1525000 1962 3 2 7 4400
2475000 1753 3 2 8 9800
1410000 1618 3 2 4 5020
1782500 1994 3 2 4 1300

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