Question: Caring for hospital patients. Any medical item used in the care of hospital patients is called a factor. For example, factors can be intravenous tubing, intravenous fluid, needles, shave kits, bedpans, diapers, dressings, medications, and even code carts. The coronary care unit at Bayonet Point Hospital (St. Petersburg, Florida) investigated the relationship between the number of factors per patient, x, and the patient's length of stay (in days), y. The data for a random sample of 50 coronary care patients are given in the following table, while a SAS printout of the simple linear regression analysis.
(a) Construct a scatterplot of the data.
(b) Find the least squares line for the data and plot it on your scatterplot.
(c) Define β1 in the context of this problem.
(d) Test the hypothesis that the number of factors per patient (x) contributes no information for the prediction of the patient's length of stay (y) when a linear model is used (use α = .05). Draw the appropriate conclusions.
(e) Find a 95% confidence interval for β1. Interpret your results.
(f) Find the coefficient of correlation for the data. Interpret your results.
(g) Find the coefficient of determination for the linear model you constructed in part b. Interpret your result.
(h) Find a 95% prediction interval for the length of stay of a coronary care patient who is administered a total of x = 231 factors.
(i) Explain why the prediction interval obtained in part h is so wide. How could you reduce the width of the interval?
