Question: A hospital administrator is reviewing the relationship between the length of in-patient stays, x, in days and the total cost of care, y, in dollars. She collected the following sample data:

(a) Construct the regression model in the form \(\hat{y}={{b}_{0}}+{{b}_{1}}x\), which is the best fit for this bivariate data. [COMMENTS & HINTS: Determine the least squares line. Round off the constant \({{b}_{0}}\) and the coefficient \({{b}_{1}}\) to the nearest whole dollar.] Document or explain your work in some reasonable manner. Use available technology to expedite calculations.]

(b) Using the aforementioned regression model, predict the total cost of care, rounding to the nearest whole dollar, based upon a five (5) day in-patient stay.

(c) Using the aforementioned regression model, predict the number of days for an in-patient stay associated with a total cost of care approximately $566.

(d) Determine the Pearson product moment correlation coefficient, r. [COMMENTS & HINTS: Document or explain your work in some reasonable manner. Round off to the nearest ten-thousandth if necessary.]

(e) What percentage of the variation is due to the linear relationship between the independent variable, x, and the dependent variable, y. [COMMENTS & HINTS: Round off to the nearest ten-thousandth, then express as a percentage to two decimal places. In other words, compute the coefficient of determination \({{r}^{2}}\).]