EC 205 Statistical Case Study Multiple Regression Analysis T

EC 205 Statistical Case Study Multiple Regression Analysis The Evaluation of Labor Needs in Naval Hospitals You have been hired to provide statistical consulting for the United States Navy. The Navy wishes to evaluate how many hours of labor per month are needed to meet its medical needs. Specifically, your responsibility is to help the Navy in describing the number of monthly labor hours used in a sample of naval hospitals. Additionally, your task will be to assess the relationship between the number of monthly labor hours used and other variables provided by a sample of twelve naval hospitals. The data set containing the sample of twelve naval hospitals is given below. The last six hospitals in the sample are teaching/training hospitals and the first six hospitals are not. In addition to type of hospital, the other study variables include: -- Hours (number of monthly labor hours used) -- X-Rays (number of monthly X-ray exposures) -- Bed-Days (number of monthly occupied bed days) -- Length (average length of a patient’s stay in days) Hospital Hours X-Rays Bed-Days Length 1 566 2463 473 4.5 2 696 2048 1339 6.9 3 1033 3940 620 4.3 4 1611 5723 1497 5.5 5 1613 11520 1365 4.6 6 3503 20106 1365 6.1 7 1603 6505 568 3.9 8 1854 5779 620 5.6 9 2160 5969 568 5.2 10 2305 8461 1497 6.2 11 3571 13313 1687 5.9 12 3741 10771 1639 4.9 I. Enter the data set containing the sample of 12 hospitals into an Excel spreadsheet. II. Type your name at the top of the spreadsheet. III. Add the Teaching/Training qualitative variable to your data set. Specifically, if a particular hospital is a teaching/training hospital, then the variable teaching/training should be set to 1 and if a hospital is not a teaching/training hospital, the variable teaching/training should be set to 0. 1. Summarize the number of monthly labor hours used in the sample of 12 hospitals using the appropriate descriptive statistics. Provide an interval estimate for the average number of monthly labor hours used for all naval hospitals. Use 95% level of confidence for the prediction. (1point) 2. As there is reason to believe that the number of monthly labor hours used may be at least partially explained by other variables, the Navy has suggested that the relationship between each of the other quantitative variables and number of monthly labor hours be assessed. (a) Graphically show the linear relationship between each of the other quantitative variables and the hours of labor used. Which of the other quantitative variables has the strongest linear relationship with hours of labor? Why?(1.5point) 3. You want to build a regression model to estimate the number of hours of labor used for a given month. Estimate the regression equation using the number of hours of labor used and the quantitative variable you selected in question 5b. (i) Provide the least squares estimated regression equation and interpret the regression coefficients.( 2.5 points) (ii) What percentage of the variation in the number of labor hours used has been explained by the estimated regression equation? Is this a useful amount? (0.5 point) (iii) How many hours of labor would be expected to be used for a naval hospital that has characteristics identical to those of hospital #1? Calculate the value of the residual. (0.5 point) 4. The Navy believes that the number of labor hours used is influenced by all the other variables in the data set. a. Estimate the multiple regression model for the data based on all of the variables including the teaching/training variable. Provide the equation. (0.5 point) b. Set up and provide the hypotheses to test whether the multiple regression model as a whole is significant. At 0.05 level of significance what is your conclusion? (1 point) c. Interpret the value of the regression coefficient for X-rays from the estimated multiple regression equation. (1point) d. Test to determine if there is a linear relationship between X-Rays and the number of monthly labor hours used . At the 0.05 level of significance, what is your conclusion? (1point) e. Use the estimated multiple regression equation to predict the number of monthly labor hours used for the first hospital in the sample. Calculate the value of the residual. (0.5 point) f. The Navy believes that Teaching/Training hospitals will have lower amount of labor hours used after adjusting for each of the other independent variables. Do your results support this belief? Why or why not? (1 point) h. Given the three estimation methods (univariate, bivariate, and multivariate) presented in this report for estimating labor hours which would you recommend be used? Why? (1 point)

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