A Realtor is interested in modeling the selling price of houses based on the square footage, the age of the house, and the style. The data was collected in the two largest cities in Arkansas and is presented in an excel file. We need two indicator variables for the style of the house. I will choose Traditional as the base category. 1 if the house is victorian rambler [ 1 if the house is a rambler 10 if not Ivictor 10 if not Now use JMP output to answer the following: 1. Plot Y vs. X] and Y vs. X2. Do you see any curvature in these 2 plots? If so what can be suggested about the variables? Which higher order terms, if any, are needed in the model? This question won't appear in the submission link, but you should make the plots and think about what higher order terms might be necessary. 2. Suppose someone wishes to use the regression model Y = Bot BIXit B2Xz + ByXi + BAX + BsX1X2+ Belrambler + Bylvictor+ = a) Write Down the prediction equation. b) Find R2 (as a %, 2 decimals) and interpret it. c) Test if the regression model is useful. (F-test) d) Calculate 95% confidence intervals for Pi and B2 (2 decimals).c) Calculate a 95% confidence interval for Po (2 decimals). Based on your interval, do you believe that a Rambler style house has a significantly higher average selling price than a Traditional style house? () Using p-values and a = 0.05, which variables are significant? 3. Now using the model Y = fo+ 1X, + 82Xi + Byrambler + Palvictor + & answer the following: (You do not have to run this model in JMP) a) What is the E(Y) when the house is a Rambler? Hrambler= b) What is the E(Y) when the house is a Traditional? Htraditional c) What is the E(Y) when the house is a Victorian? Hvictor= d) Find: Hrambler - Htraditional e) Find: victor - Htraditional f) Find: Hrambler - AvictorClipboard Font Alignment Number N14 X V fx A B C D E F G H J K 1 Y X1 X2 X3 Irambler Ivictor X1-5q X2-5q X1X2 28000 775 37 Traditional 600625 1369 28675 34000 700 49 Traditional 0 0 0 490000 2401 34300 34500 720 54 Traditional 518400 2916 38880 39900 864 37 Rambler 0 746496 1369 31968 40000 650 35 Traditional 422500 1225 22750 -O 41500 780 79 Victorian 608400 6241 61620 42500 900 48 Traditional 810000 2304 43200 0O 9 53500 816 35 Rambler 665856 1225 28560 10 57000 1800 17 Victorian 3240000 289 30600 11 59000 1340 66 Victorian 0-060-06-06-060 -0 0 0 1795600 4356 88440 12 59500 1800 18 Rambler O 3240000 324 32400 13 62000 1124 34 Traditional 1263376 1156 38216 14 68500 2880 24 Victorian 8294400 576 69120 15 72500 1480 75 Rambler 0 2190400 5625 111000 16 70000 1652 94 Victorian 2729104 8836 155288 17 73112 2088 71 Victorian 4359744 5041 148248 18 76780 1700 34 Traditional 0 2890000 1156 57800 19 77350 1262 78 Rambler 1592644 6084 98436 20 85590 1500 54 Victorian 2250000 2916 81000 21 79900 1200 35 Victorian 1440000 1225 42000 22 48100 650 45 Traditional 422500 2025 29250 23 24 25QUESTION 1 Write Down the prediction equation. O a. Y_hat = -36729 +76.2*X1 O b. Y_hat = -36729 +76.2*X1 + 1143*X2 + 5496*Irambler +5225*Ivictor O c. Y_hat = -36729 +76.2*X1 + 1143*X2 - 0.01781*X1 2 - 10.58*X2 2 + 0.04*X1*X2 O d. Y_hat = -36729 +76.2*X1 + 1143*X2 - 0.01781*X1^2 -10.58*X2 2 + 0.04*X1*X2 + 5496*Irambler +5225*Ivictor QUESTION 2 Find R2. 67.409% QUESTION 3 Interpret R2. O a. about 72% of the variation in Y is explained by the model. O b. The correlation between X1 and Y is 0.7228. O c. There is about a 72 percent chance that our predictions are accurate. O d. About 729% of home sale prices are below $50,000.QUESTION 4 Test if the regression model is useful. (F-test) O a. Reject Ho, there is no evidence that the model is useful. O b. Reject Ho, there is evidence that the model is useful. O c. Do not reject Ho, there is no evidence that the model is useful. O d. Do not reject Ho, there is evidence that the model is useful. QUESTION 5 Does your interval for B1 include 0? O a. Yes O b. No QUESTION 6 Does your interval for B2 contain 0? O a. Yes O b. No QUESTION 7 Does your interval for B6 contain 0? O a. Yes O b. NoQUESTION 8 Which variables are significant with alpha = 0.05? O a. All of them O b. None of them O c. Only X1 and X2 O d. Only X1 and X12 QUESTION 9 What is the E(Y) when the house is a Rambler? O a. BO + B1*X1 + B2*X1^2 + B4 O b. B0 + B1*X1 + B2*X1^2 O c. B0 + B1*X1 + B2*X1^2 + B3 O d. BO QUESTION 10 What is the E(Y) when the house is a Traditional? O a. B0 + B1*X1 + B2*X1/2 + B4 O b. B0 + B1*X1 + B2*X1^2 O c. BO + B1*X1 + B2*X1/2 + B3 O d. BOQUESTION 11 What is the E(Y) when the house is a Victorian? O a. BO + B1*X1 + B2*X1/2 + B4 O b. B0 + B1*X1 + B2*X1^2 O c. B0 + B1*X1 + B2*X1/2 + B3 O d. BO QUESTION 12 Find: Hrambler - Htraditional O a. B3 O b. B4 O c. B1 O d. B2 QUESTION 13 Find: Hvictor - Htraditional O a. B2 O b. B3 O c. BO O d. B4QUESTION 13 Find: Hvictor - Htraditional O a. B2 O b. B3 O c. BO O d. B4 QUESTION 14 Find: Hrambler - Hvictor O a. B2 - B4 O b. B3 - B4 O c. B1 - B3 O d. BO