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. Click the icon to view the 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. Sales Price = 108726 + ( 3.68 ) . Lot Cost + ( - 75,063 ) . Townhouse (Round the constant and coefficient of Townhouse to the nearest integer as needed. Round all other values to two decimal places as needed.) b. Determine if an interaction exists between lot cost and type of home and find the best model. Use o = 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 is , which is greater than a. (Type an integer or a decimal rounded to three decimal places as needed.) O B. An interaction exists because the p-value of the variable Lot Cost . Townhouse is , which is less than a. Type an integer or a decimal rounded to three decimal places as needed.) O C. An interaction exists because the p-value of the variable Townhouse is , which is greater than a. 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.Type Sales Price Lot Cost Townhouse $114,740 $21,700 Single Family $138,530 $26,550 Townhouse $149,905 $25,550 Single Family $172,000 $26,200 Townhouse $183,916 $46,025 Townhouse $189,390 $28,000 Single Family $191,120 $36,000 Townhouse $198,898 $46,025 Townhouse $205,076 $46,025 Single Family $207,821 $40,299 Single Family $216,205 $37,500 Townhouse $252,800 $74,400 Single Family $257,000 $44,198 Single Family $270,000 $44,344 Single Family $270,500 $42,099 Single Family $273, 105 $46,000 Single Family $279,720 $45,650 Single Family $296,990 $58,000 Single Family $303,500 $60,000 Single Family $309,487 $46,850 Single Family $314,898 $41,768 Single Family $321,602 $83,300 Single Family $326,412 $63,523 Single Family $339,374 $71,449 Single Family $339,380 $50,150 Single Family $340,065 $55,850 Single Family $356,117 $57,219 Single Family $361,949 $51,591 Single Family $434,426 $58,422 Single Family $494,820 $85,122