Exercise 4: Tommorow A specialist in hospital administration stated that the number of full-time em- ployees (FTEs) in a hospital can be estimated by counting the number of beds in the hospital (a common measure of hospital size). A health-care business an- alyst decided to develop a regression model in an attempt to predict the number of FTEs of a hospital by the number of beds. She surveyed 12 hospitals and obtained the following data. The data are presented in sequence, according to the number of beds. 1333333 Number of Beds Full-Time Employees 69 95 102 118 126 125 138 178 156 184 176 225 mp 1. Determine the value of the correlation coefficient for these data. 2. Does it appear reasonable to use a simple linear regression model to de- scribe the association between number of FTEs of a hospital and number of beds? If so, find the least squares equation of the regression line. 3. Compute the residuals for this model. Do they appear to be normally dis- tributed? Calculate the standard error estimate for this statistical model. 4. Test the slope of this statistical model to determine whether there is a significant positive slope. Use a = 0.01. 5. Construct a 95% confidence interval to estimate the average value of FTEs when the number of beds is 40.