National homebuilder build 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

without any interaction term.

b$)$ Determine if an interaction exists between lot cost and type of home and find the best model.

c$)$ What is the predicted price for either a single$-$family home or a townhouse with $\backslash$table$[[4,$A$,B,$L$,$D$,$E$],[1,$House Sales $\frac{x}{?}$ sx$,,,,],[2,,,,,],[3,$Region,Type,Selling Price,Lot Cost,$],[4,$Midwest,Townhouse,$$85,145,$$$17,030,],[5,$Midwest,Townhouse,$$112,740,$$$20,700,],[6,$Midwest,Townhouse,$$115,350,$$$18,030,],[7,$Midwest,Townhouse,$$116,415,$$$19,600,],[8,$Midwest,Townhouse,$$133,070,$$$24,455,],[9,$Midwest,Single Family,$$136,530,$$$25,500,],[10,$Midwest,Townhouse,$$139,435,$$$29,155,],[11,$Midwest,Townhouse,$$139,955,$$$30,400,],[12,$Midwest,Townhouse,$$147,905,$$$24,650,],[13,$Midwest,Single Family,$$153,845,$$$27,500,],[14,$Midwest,Townhouse,$$155,270,$$$19,600,],[15,$Midwest,Townhouse,$$155,870,$$$24,650,],[16,$South,Single Family,$$160,000,$$$29,500,],[17,$Midwest,Single Family,$$165,220,$$$25,500,],[18,$Midwest,Single Family,$$165,350,$$$25,000,],[19,$Midwest,Single Family,$$168,354,$$$27,316,],[20,$Midwest,Single Family,$$168,500,$$$33,000,],[21,$Midwest,Single Family,$$170,000,$$$25,200,],[22,$South,Townhouse,$$172,749,$$$45,025,],[23,$Midwest,Single Family,$$175,000,$$$28,000,],[24,$Midwest,Townhouse,$$175,470,$$$28,600,],[25,$Midwest,Townhouse,$$179,365,$$$32,200,],[26,$South,Townhouse,$$181,916,$$$45,025,],[27,$South,Townhouse,$$182,237,$$$45,025,],[28,$Midwest,Single Family,$$183,370,$$$28,000,],[29,$Midwest,Single Family,$$184,210,$$$28,000,],[30,$Midwest,Single Family,$$184,460,$$$22,300,],[31,$Midwest,Townhouse,$$184,873,$$$33,400,],[32,$Midwest,Single Family,$$185,160,$$$29,000,],[33,$South,Single Family,$$186,000,$$$35,851,],[34,$Midwest,Townhouse,$$187,390,$$$27,000,],[35,$Midwest,Single Family,$$188,603,$$$31,300,],[36,$Midwest,Single Family,$$189,120,$$$35,000,],[37,$South,Single Family,$$191,028,$$$45,000,],[38,$South,Townhouse,$$196,898,$$$45,025,],[39,$South,Townhouse,$$198,202,$$$45,025,],[4n,$Snuth,Sinnle Familv,$sin119,$SA$5$n$,],[,,\backslash$table$[[8\mathrm{.}5,8\mathrm{.}11]],8\mathrm{.}17,8\mathrm{.}21,3\mathrm{.}3]]$

a lot cost of $$30,000?$