Data for hospital bills X Full Data Set O Costs ($) | Age Days ICU Costs ($) Age Days ICU 1433 20 1 0 10670 41 6 2 1948 37 1 0 9718 41 4 2705 35 3 10055 75 4 2835 28 3 0 10654 25 2 3197 39 1 0 10695 68 3 3618 23 2 12264 37 5 3982 27 12353 47 4348 46 12553 28 7 4707 28 12657 71 4 4873 38 12948 37 6 5107 28 3 13183 79 5 5758 34 2 13498 67 8 6338 47 4 0 13515 34 7 6640 29 4 18340 55 14 6785 31 1 0 17048 57 7 INONE 6920 22 3 0 18376 39 11 7766 25 1 18826 86 6 0 9734 59 3 0 17385 53 8 9062 31 6 20378 46 4 0 7993 52 1 0 14569 37 11 0 8021 42 3 0 28462 57 8 8198 33 0 28701 60 17 8493 21 6 0 22425 54 9 9281 20 2 32560 49 12 9373 40 7 0 34216 69 9 2A hospital would like to develop a regression model to predict the total hospital bill for a patient based on the age of the patient (x, ), his or her length of stay (x2 ), and the number of days in the hospital's intensive care unit (ICU) (*;). Data for these variables can be found in the accompanying table. Complete parts a through e below. Click the icon to view the data for a random selection of patients. a) Construct a regression model using all three independent variables. y = (0) +(0) * +() *2 + (0)*3 (Round to the nearest whole number as needed.) b) Interpret the meaning of the regression coefficients. Select the correct choice below and, if necessary, fill in the answer boxes within your choice. (Round to the nearest dollar as needed.) J A. Each additional day of hospitalization decreases the hospital bill by $ . Each additional year of age decreases the hospital bill by $ . Each additional day spent in the ICU decreases the hospital bill by $ J B. Each additional year of age increases the hospital bill by $ . Each additional day of hospitalization increases the hospital bill by $ . Each additional day spent in the ICU increases the hospital bill by S. O C. There is no meaningful interpretation of the regression coefficients for this application. c) Predict the average hospital bill for a 76-year-old person hospitalized for four days with one day spent in the ICU. y =$(Round to the nearest dollar as needed.) d) Construct a 95% confidence interval for the average hospital bill for the patient described in part c. Interpret the meaning of the interval. The 95% confidence interval is from a lower limit of | | dollars to an upper limit of | dollars. Round to the nearest dollar as needed.) Interpret the meaning of the interval. Choose the correct answer below A. The hospital bill for a 76-year-old person hospitalized for four days with one day spent in the ICU is between the lower and upper limits of the 95% confidence interval 95% of the time. O B. It can be stated with 95% confidence that the average hospital bill for a 76-year-old person hospitalized for four days with one day spent in the ICU is between the lower and upper limits of the 95% confidence interval. O C. It can be stated with 95% confidence that the hospital bill for a 76-year-old person hospitalized for four days with one day spent in the ICU is between the lower and upper limits of the 95% confidence interval. O D. The average hospital bill for a 76-year-old person hospitalized for four days with one day spent in the ICU is between the lower and upper limits of the 95% confidence interval 95% of the time.e) Construct a 95% prediction interval for the average hospital bill for the patient described in part c, that is, a 76-year-old person hospitalized for four days with one day spent in the ICU. The 95% prediction interval is from a lower limit of | dollars to an upper limit of |dollars. (Round to the nearest dollar as needed.) Interpret the meaning of the interval. Choose the correct answer below O A. The hospital bill for a 76-year-old person hospitalized for four days with one day spent in the ICU is between the lower and upper limits of the 95% confidence interval 95% of the time. O B. The average hospital bill for a 76-year-old person hospitalized for four days with one day spent in the ICU is between the lower and upper limits of the 95% confidence interval 95% of the time. O C. It can be stated with 95% confidence that the hospital bill for a particular 76-year-old person hospitalized for four days with one day spent in the ICU is between the lower and upper limits of the 95% prediction interval. D. It can be stated with 95% confidence that the average hospital bill for a 76-year-old person hospitalized for four days with one day spent in the ICU is between the lower and upper limits of the 95% prediction interval