(Problem 27 in Chapter 6 (Page 206) in [E2012]) A national homebuilder builds single-family homes and condominium-style townhouses. The Excel file House Sales provides information on the selling price, lot cost, type of home, and region of the country (M=Midwest, S=South) for closings during one month.

a. Develop a multiple regression model for sales price as a function of lot cost and type of home.

b. Determine if any interactions exist between lot cost and type of home, and find the best model.

c. Develop a regression model for selling price as a function of lot cost and region. (Note that the categorical variable region has more than two levels.)

Region Midwest Midwest Midwest Midwest Midwest Midwest Midwest Midwest Midwest Midwest Midwest Midwest South Midwest Midwest Midwest Midwest Midwest South Midwest Midwest Midwest South South Midwest Midwest Midwest Midwest Midwest South Midwest Midwest Midwest South South South South South Midwest South South Midwest South South South South South Midwest Midwest South Type Townhouse Townhouse Townhouse Townhouse Townhouse Single Family Townhouse Townhouse Townhouse Single Family Townhouse Townhouse Single Family Single Family Single Family Single Family Single Family Single Family Townhouse Single Family Townhouse Townhouse Townhouse Townhouse Single Family Single Family Single Family Townhouse Single Family Single Family Townhouse Single Family Single Family Single Family Townhouse Townhouse Single Family Townhouse Single Family Single Family Townhouse Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Selling Price Lot Cost $85,145 $17,030 $112,740 $20,700 $115,350 $18.030 $116,415 $19,600 $133,070 $24.455 $136,530 $25,500 $139,435 $29,155 $139,955 $30,400 $147,905 $24,650 $153,845 $27,500 $155,270 $19,600 $155,870 $24,650 $160,000 $29,500 $165,220 $25,500 $165,350 $25,000 $168,354 $27.316 $168,500 $33,000 $170,000 $25,200 $172,749 $45,025 $175,000 $28,000 $175,470 $28,600 $179,365 $32,200 $181.916 $45,025 $182,237 $45.025 $183,370 $28,000 $184,210 $20,000 $184,460 $22,300 $184,873 $33,400 $185,160 $29.000 $186,000 $35,851 $187,390 $27,000 $188,603 $31,300 $189,120 $35,000 $191,028 $45.000 $196,896 $45,025 $198,202 $45,025 $200,119 $45,000 $200,423 $45,025 $201.700 $40,940 $202,000 $31,160 $203,076 $45,025 $203,950 $33,000 $204,900 $34,000 $205,821 $39,299 $206,400 $35,851 $207,345 $35,600 $209,400 $43,579 $210,380 $33,856 $211,513 $31,300 $211,797 $34,000 Midwest South Midwest South South Midwest Midwest South South South South Midwest Midwest Midwest South South South South South South South Midwest South Midwest South South South South South South South South Midwest Sou South Midwest South South South South Midwest South South South Midwest Midwest South Midwest South South Midwest Townhouse Single Family Single Family Single Family Single Family Single Family Single Family Townhouse Single Family Single Family Townhouse Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Townhouse Single Family Single Family Single Family Single Family Single Family Single Family Townhouse Single Family Single Family Single Family Townhouse Townhouse Single Family Townhouse Single Family Single Family Single Family Townhouse Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family $212,079 $33,400 $214,205 $36,500 $214,900 $31,300 $216,049 $35,600 $219,990 $37,557 $220,257 $31,300 $223,890 $20,000 $224,108 $45.025 $225,900 $28,618 $226,000 $35,600 $230,000 $45,025 $230,440 $33,000 $230,555 $28.000 $233,900 $44,200 $234,971 $29,202 $239,000 $39.169 $239,870 $41,354 $241,195 $41,340 $242,191 $33,434 $242,899 $48.252 $246,648 $41,600 $248,500 $20,000 $249,900 $38,200 $250,005 $33,000 $250,000 $73,400 $252,195 $41,341 $253,055 $41,340 $254,048 $39,630 $255,000 $43,198 $256,235 $48,500 $257,040 $37,631 $260,100 $73,400 $262,740 $44,900 $262,890 $48,500 $265,058 $41,404 $265,500 $35,800 $267,060 $73,400 $267,250 $45,676 $267,640 $73,400 $268,000 $43,344 $268,210 $29,700 $268,500 $41,099 $269,410 $73,400 $270,518 $46,499 $271,105 $45,000 $274,455 $41,000 $274,903 $45,345 $277,720 $44,650 $280,622 $45,130 $280,804 $40,667 $281,487 $57,285 South Midwest South South Midwest South South South South South South South Midwest South South South South South South South South South South Midwest South South South South Midwest South South South South South South South South South Midwest South South South South South South South South South South South South Single Family Single Family Single Family Single Family Single Family Single Family Single Family Townhouse Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Townhouse Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family $281.824 $50,448 $283,440 $50,900 $286,756 $57,000 $287,771 $46,300 $289,000 $44,000 $290,000 $48,300 $290,190 $82,250 $294,450 $73,400 $294.990 $57,000 $299,096 $43,784 $301,500 $59,000 $305,000 $49,067 $307,373 $41,292 $307,387 $45,850 $307,663 $44,840 $309,075 $82,250 $310,100 $41,800 $310,372 $60,000 $312,898 $40.768 $318,274 $85,800 $318,523 $50,000 $319,602 $82,250 $322,920 $82,250 $323,716 $34,500 $324,266 $47,891 $324,412 $62,523 $326,570 $51,000 $329,611 $48,611 $330,486 $35.000 $330,710 $49.920 $333,156 $49,123 $335,000 $68,375 $337,374 $70,399 $337,380 $49,150 $338,065 $54,850 $340,000 $40,000 $340,730 $50,850 $342,423 $48,309 $348,744 $53,000 $350,702 $46,336 $352,781 $60,000 $354,065 $48.115 $354,117 $56,219 $355,688 $65.373 $358,162 $44.470 $359,949 $50,591 $366,990 $55,508 $367,600 $50,000 $369,101 $46.773 $371,152 $58.223 $379,000 $72.915 South South South South South South South South South Midwest South South South South South South Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family $379,424 $64.902 $379,575 $44,294 $385,000 $75,000 $385,942 $49,123 $387,527 $48,000 $398,651 $65,429 $400,330 $75,510 $404,510 $58,225 $407,076 $48,668 $410,810 $66,500 $417,790 $63,099 $432,426 $57,422 $444,304 $53,938 $446,507 $75,510 $492,820 $84,122 $575,120 $79,790 Region Midwest Midwest Midwest Midwest Midwest Midwest Midwest Midwest Midwest Midwest Midwest Midwest South Midwest Midwest Midwest Midwest Midwest South Midwest Midwest Midwest South South Midwest Midwest Midwest Midwest Midwest South Midwest Midwest Midwest South South South South South Midwest South South Midwest South South South South South Midwest Midwest South Type Townhouse Townhouse Townhouse Townhouse Townhouse Single Family Townhouse Townhouse Townhouse Single Family Townhouse Townhouse Single Family Single Family Single Family Single Family Single Family Single Family Townhouse Single Family Townhouse Townhouse Townhouse Townhouse Single Family Single Family Single Family Townhouse Single Family Single Family Townhouse Single Family Single Family Single Family Townhouse Townhouse Single Family Townhouse Single Family Single Family Townhouse Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Selling Price Lot Cost $85,145 $17,030 $112,740 $20,700 $115,350 $18.030 $116,415 $19,600 $133,070 $24.455 $136,530 $25,500 $139,435 $29,155 $139,955 $30,400 $147,905 $24,650 $153,845 $27,500 $155,270 $19,600 $155,870 $24,650 $160,000 $29,500 $165,220 $25,500 $165,350 $25,000 $168,354 $27.316 $168,500 $33,000 $170,000 $25,200 $172,749 $45,025 $175,000 $28,000 $175,470 $28,600 $179,365 $32,200 $181.916 $45,025 $182,237 $45.025 $183,370 $28,000 $184,210 $20,000 $184,460 $22,300 $184,873 $33,400 $185,160 $29.000 $186,000 $35,851 $187,390 $27,000 $188,603 $31,300 $189,120 $35,000 $191,028 $45.000 $196,896 $45,025 $198,202 $45,025 $200,119 $45,000 $200,423 $45,025 $201.700 $40,940 $202,000 $31,160 $203,076 $45,025 $203,950 $33,000 $204,900 $34,000 $205,821 $39,299 $206,400 $35,851 $207,345 $35,600 $209,400 $43,579 $210,380 $33,856 $211,513 $31,300 $211,797 $34,000 Midwest South Midwest South South Midwest Midwest South South South South Midwest Midwest Midwest South South South South South South South Midwest South Midwest South South South South South South South South Midwest Sou South Midwest South South South South Midwest South South South Midwest Midwest South Midwest South South Midwest Townhouse Single Family Single Family Single Family Single Family Single Family Single Family Townhouse Single Family Single Family Townhouse Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Townhouse Single Family Single Family Single Family Single Family Single Family Single Family Townhouse Single Family Single Family Single Family Townhouse Townhouse Single Family Townhouse Single Family Single Family Single Family Townhouse Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family $212,079 $33,400 $214,205 $36,500 $214,900 $31,300 $216,049 $35,600 $219,990 $37,557 $220,257 $31,300 $223,890 $20,000 $224,108 $45.025 $225,900 $28,618 $226,000 $35,600 $230,000 $45,025 $230,440 $33,000 $230,555 $28.000 $233,900 $44,200 $234,971 $29,202 $239,000 $39.169 $239,870 $41,354 $241,195 $41,340 $242,191 $33,434 $242,899 $48.252 $246,648 $41,600 $248,500 $20,000 $249,900 $38,200 $250,005 $33,000 $250,000 $73,400 $252,195 $41,341 $253,055 $41,340 $254,048 $39,630 $255,000 $43,198 $256,235 $48,500 $257,040 $37,631 $260,100 $73,400 $262,740 $44,900 $262,890 $48,500 $265,058 $41,404 $265,500 $35,800 $267,060 $73,400 $267,250 $45,676 $267,640 $73,400 $268,000 $43,344 $268,210 $29,700 $268,500 $41,099 $269,410 $73,400 $270,518 $46,499 $271,105 $45,000 $274,455 $41,000 $274,903 $45,345 $277,720 $44,650 $280,622 $45,130 $280,804 $40,667 $281,487 $57,285 South Midwest South South Midwest South South South South South South South Midwest South South South South South South South South South South Midwest South South South South Midwest South South South South South South South South South Midwest South South South South South South South South South South South South Single Family Single Family Single Family Single Family Single Family Single Family Single Family Townhouse Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Townhouse Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family $281.824 $50,448 $283,440 $50,900 $286,756 $57,000 $287,771 $46,300 $289,000 $44,000 $290,000 $48,300 $290,190 $82,250 $294,450 $73,400 $294.990 $57,000 $299,096 $43,784 $301,500 $59,000 $305,000 $49,067 $307,373 $41,292 $307,387 $45,850 $307,663 $44,840 $309,075 $82,250 $310,100 $41,800 $310,372 $60,000 $312,898 $40.768 $318,274 $85,800 $318,523 $50,000 $319,602 $82,250 $322,920 $82,250 $323,716 $34,500 $324,266 $47,891 $324,412 $62,523 $326,570 $51,000 $329,611 $48,611 $330,486 $35.000 $330,710 $49.920 $333,156 $49,123 $335,000 $68,375 $337,374 $70,399 $337,380 $49,150 $338,065 $54,850 $340,000 $40,000 $340,730 $50,850 $342,423 $48,309 $348,744 $53,000 $350,702 $46,336 $352,781 $60,000 $354,065 $48.115 $354,117 $56,219 $355,688 $65.373 $358,162 $44.470 $359,949 $50,591 $366,990 $55,508 $367,600 $50,000 $369,101 $46.773 $371,152 $58.223 $379,000 $72.915 South South South South South South South South South Midwest South South South South South South Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family Single Family $379,424 $64.902 $379,575 $44,294 $385,000 $75,000 $385,942 $49,123 $387,527 $48,000 $398,651 $65,429 $400,330 $75,510 $404,510 $58,225 $407,076 $48,668 $410,810 $66,500 $417,790 $63,099 $432,426 $57,422 $444,304 $53,938 $446,507 $75,510 $492,820 $84,122 $575,120 $79,790