Question

4)A hospital administrator developed a regression line, y = 30 + 2x, to predict the number of full-time

employees (FTE) needed using the number of beds. The slope of this regression line suggests this: ___

Answer 1

The slope of the regression line is 2. This means that for every additional bed, 2 additional full-time employees are needed.

Step-by-step explanation:

1. We must first identify the slope by referencing the equation of a line:
`y=mx+b`.

• The regression line given is written in a different order:
  `y=b+mx`.
• Whatever number is attached to the variable, x, is the slope. Therefore, m = 2.

2. Next, we must identify the units for y and x. Based on the sentence "to predict the number of full-time employees needed using the number of beds," we can assume that y = # of full-time employees and x = # of beds. This is because the number of full-time employees is being predicted, or in other words, calculated. Furthermore, this calculation is dependent on the number of beds, meaning that this value must be within the equation to calculate. Therefore:

• y = # of full-time employees
• x = # of beds

3. Using the units we found in Step 2 and the slope determined in Step 1, we can determine the meaning of the slope by observing the equation. For the purpose of understanding the slope, we can ignore the b-value (+30). When doing so, we get the equation y = 2x. From here, when plugging in numbers, we can recognize that for every increase in x (# of beds), y (# of full-time employees) increases by 2. Therefore, the slope means that For every bed, there are 2 full-time employees.

Answer 2

The slope of the regression line y = 30 + 2x suggests a positive relationship between the number of beds and the number of full-time employees needed.

Step-by-step explanation:

The slope of the regression line, y = 30 + 2x, suggests that for every one unit increase in the number of beds (x), the number of full-time employees (y) needed increases by 2 units. In other words, the slope of 2 indicates a positive relationship between the number of beds and the number of full-time employees. This means that as the number of beds increases, the hospital administrator predicts that more full-time employees will be needed.