A hospital would like to develop a regression model to predict the total hospital bill for a patient based on his or her length of?stay, number of days in the?hospital's intensive care unit?(ICU), and age of the patient. Data for these variables can be found in the accompanying table. Complete parts?(a) through?(e) below.
\fA hospital would like to develop a regression model to predict the total hospital bill for a patient based on his or her length of stay, number of days in the hospital's intensive care unit (ICU), and age of the patient. Data for these variables can be found in the accompanying table. Complete parts (a) through (e) below. Click the icon to view the data table. a) Using technology, construct a regression model using all three independent variables, where y = Cost, x, = Age, X2 = Days, and *3 = ICU. (Round to the nearest integer as needed.) b) Test the significance of each independent variable using a = 0.10. Identify the general form of the null and alternative hypotheses, where @ is the population regression coefficient for the jth independent variable. Ho : P H1 : Pi Find the test statistic for the coefficient of each independent variable. Variable t *1 Xa X3 (Round to two decimal places as needed.) Find the p-value for the coefficient of each independent variable. Variable p-valueVariable p-value X2 X3 (Round to three decimal places as needed. ) Interpret the p-value for the hypothesis test corresponding to X1. Since the p-value associated with x, is 0 = 0.10. the null hypothesis. There is evidence to conclude that there a relationship between x, and y. Interpret the p-value for the hypothesis test corresponding to x2- Since the p-value associated with x2 is 0 =0.10. the null hypothesis. There is evidence to conclude that there a relationship between x2 and y. Interpret the p-value for the hypothesis test corresponding to x3. Since the p-value associated with x3 is 0 = 0.10. the null hypothesis. There is evidence to conclude that there a relationship between x3 and y. c) Interpret the p-value for each independent variable. Choose the correct answer below. A. According to the p-values, only the independent variable x2 has a relationship with y. O B. According to the p-values, the independent variables x, and x2 have a relationship with y. C. According to the p-values, the independent variables X1, X2 and x3 have a relationship with y.c) Interpret the p-value for each independent variable. Choose the correct answer below. O A. According to the p-values, only the independent variable xy has a relationship with y. O B. According to the p-values, the independent variables x, and xz have a relationship with y. O C. According to the p-values, the independent variables x1. x2 and x3 have a relationship with y. O D. According to the p-values, only the independent variable x, has a relationship with y. d) Construct a 90% confidence interval for the regression coefficient for the ICU variable, x3. in terms of expected costs. The 90% confidence interval is from ] to (] (Round to the nearest integer as needed.) State the 90% confidence interval for the regression coefficient for the ICU variable in terms of expected costs. Choose the correct answer below. O A. One can be 90% confident that a 1% increase in the average total hospital bill will cause the bill to be between the lower confidence limit and the upper confidence limit, in dollars, if all other variables are held constant. B. One can be 90%% confident that the average total hospital bill will be between the lower confidence limit and the upper confidence limit, in dollars, if all other variables are held constant O C. The confidence interval indicates the range of the average total hospital bill if the value of the ICU variable is 0, with 90% confidence, if all other variables are held constant. O D. One can be 90% confident that an extra 1 day stay in the hospital's ICU will change the average total hospital bill between the lower confidence limit and the upper confidence limit, in dollars, if all other variables are held constant. e) Using the results from part (d), comment on the significance of the x, variable. Since the confidence interval 0. there is evidence to conclude that the true population coefficient, 3. is not 0 and that there a relationship between the number of days spent in the ICU and the total hospital bill
