A national homebuilder builds single-family homes and condominium-style townhouses. The accompanying dataset provides information on the selling price, lot cost, and type of home for closings during one month. Complete parts a through c.E Click the icon to view the house sales data.House sales dataa. Develop a multiple regression model for sales price as a function of lot cost and type of home without any interaction term.Create a dummy variable named "Townhouse", where it is equal to 1 when Type = "Townhouse" and 0 otherwise. Determine the coefficients of the regression equation.ТуреTownhouseSales PriceLot CostSales Price = 108726 + ( 3.68 )• Lot Cost + ( - 75063 )• Townhouse$114,740$138,530$21,700$26,550Single FamilyTownhouseSingle FamilyTownhouse(Round the constant and coefficient of Townhouse to the nearest integer as needed. Round all other values to two decimal places as needed.)$149,905$172.000$25,550$26,200b. Determine if an interaction exists between lot cost and type of home and find the best model. Use a = 0.1 as the level of significance.$183,916$189.390$46,025lownhouseSingle FamilyTownhouseS28,000$36,000$46,025$46,025$40 299First determine whether an interaction exists. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.$191,120191,120$198,898C A. An interaction exists because the p-value of the variable Lot Cost • Townhouse is 0.091, which is less than a.(Type an integer or a decimal rounded to three decimal places as needed.)$205.076$207,821$216.205TownhouseSingle FamilySingle FamilyTownhouseSingle FamilySingleO B. An interaction exists because the p-value of the variable Townhouse is(Type an integer or a decimal rounded to three decimal places as needed.)which is greater than a.$37,500$252,800$74,400$44,198$257,000$270.000O C. An interaction exists because the p-value of the variable Lot Cost is(Type an integer or a decimal rounded to three decimal places as needed.)which is greater than a.FamilySingle$44.344$42,099FamilySingle FamilySingle$270,500$273,105$279,720$296.990$303.500$46.000O D. No interaction exists because the p-value is less than a for all of the independent variables.FamilySingle FamilySingle FamilySingle FamilySingle FamilyFamíly$45,650$58,000Now identify the best model and determine the coefficients of the regression equation. Select the correct choice below and fill in the answer boxes to complete your choice.(Round the constant and coefficient of Townhouse to the nearest integer as needed. Round all other values to two decimal places as needed.)$60.000$309,487$46.850$314,898$321,602$326,412$339,374$339,380$340,065$356,117$361,949$434,426$494,820$41.768O A. Sales Price =)• Townhouse +)• Lot Cost + ()• Lot Cost • TownhouseSingleFamily$83,300$63,523$71,449$50,150$55.850$57,219$51,591O B. Sales Price =+()• Townhouse + ()• Lot Cost • TownhouseFamilyO C. Sales Price =+ (|)• Lot Cost + ()• TownhouseSingle FamiFamilySingle FamilySingle FamilySingle FamilySingle Family$58.422$85,122PrintDone

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E Click the icon to view the house sales data. House sales data a. Develop a multiple regression model for sales price as a function of lot cost and type of home without any interaction term. Create a dummy variable named "Townhouse", where it is equal to 1 when Type = "Townhouse" and 0 otherwise. Determine the coefficients of the regression equation. Lot Cost $21,700 $26,550 Sales Price $114,740 Single Family $138,530 $149,905 $172,000 $183,916 $189,390 Single Family $191,120 $198,898 $205,076 $207,821 $216,205 $252,800 Single Family $257,000 $270,000 Single Family $270,500 Single Family $273,105 Single Family $279,720 $296,990 Single Family $303,500 Single Family $309,487 $314,898 $321,602 $326,412 Single Family $339,374 $339,380 $340,065 $356,117 $361,949 Single Family $434,426 $494,820 Туре Townhouse Sales Price = 108726 +(3.68 )• Lot Cost + (- 75063 ) • Townhouse (Round the constant and coefficient of Townhouse to the nearest integer as needed. Round all other values to two decimal places as needed.) Townhouse Single Family Townhouse Townhouse $25,550 $26,200 $46,025 $28,000 $36,000 $46,025 $46,025 $40,299 $37,500 b. Determine if an interaction exists between lot cost and type of home and find the best model. Use a = 0.1 as the level of significance. First determine whether an interaction exists. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. An interaction exists because the p-value of the variable Lot Cost Townhouse is 0.091, which is less than a. (Type an integer or a decimal rounded to three decimal places as needed.) Townhouse Townhouse O B. An interaction exists because the p-value of the variable Townhouse i (Type an integer or a decimal rounded to three decimal places as needed.) Single Family Single Family s , which is greater than a Townhouse $74,400 $44,198 $44,344 $42,099 $46.000 $45,650 $58,000 $60,000 $46,850 $41,768 $83,300 $63,523 $71,449 $50,150 $55,850 $57,219 $51.591 $58,422 O C. An interaction exists because the p-value of the variable Lot Cost is which is greater than a. Single Family (Type an integer or a decimal rounded to three decimal places as needed.) O D. No interaction exists because the p-value is less than a for all of the independent variables. Single Family Now identify the best model and determine the coefficients of the regression equation. Select the correct choice below and fill in the answer boxes to complete your choice. (Round the constant and coefficient of Townhouse to the nearest integer as needed. Round all other values to two decimal places as needed.) Single Family Single Family Single Family O A. Sales Price =+)• Townhouse + )• Lot Cost + ()• Lot Cost - Townhouse O B. Sales Price =+()• Townhouse +). Lot Cost Townhouse Single Family Single Family Single Family Single Family OC. Sales Price = +)• Lot Cost + () Townhouse Single Family $85,122 Print Done