Question

A hospital administrator developed a regression line, y = 30 + 2x, to predict y = the number of full-time employees (FTE) needed using x = the number of beds. The slope of this regression line suggests this: __________.

Answer 1

The slope of the regression line y = 30 + 2x shows a direct relationship between the number of beds and the FTE needed, increasing by 2 employees for every additional bed.

Step-by-step explanation:

The slope of the regression line y = 30 + 2x suggests that for each additional bed (x), the number of full-time employees (FTE) needed (y) increases by 2. This positive slope indicates a direct relationship between the number of beds and the FTE required. The slope value of 2 implies that if the number of beds increases by 1, then the hospital would need to hire 2 more full-time employees to meet the demands. The slope here does not just help in prediction, it also illustrates the sensitivity of the dependent variable (FTE) to changes in the independent variable (number of beds).

Furthermore, the regression equation reveals that even if there are no beds (when x = 0), the hospital would still need 30 full-time employees, indicated by the y-intercept of 30. This may account for administrative and other essential staff that are required regardless of the number of patients.