Question

A manager is assessing the correlation between the number of employees in a plant and the number of products produced monthly. The table below shows the data: Number of employees (x) 0 10 20 30 40 50 60 70 80 Number of products (y) 120 200 280 360 440 520 600 680 760 Part A: Is there any correlation between the number of employees in the plant and the number of products produced monthly? Justify your answer. (4 points) Part B: Write a function which best fits the data. (3 points) Part C: What does the slope and y-intercept of the plot indicate? (3 points)

Answer 1

Answer:

A) In the table, we can see that from one pair (x,y) to the next one, x-variable increase in 10 units and y-variable increase in 80 units. This is valid for all pairs (x,y), which mean that there is a linear relationship between these variables.

B) slope (m) = y-variable increment / x-variable increment = 80/10 = 8

the coordintae (0, 120) indicates that 120 is the y-intercept (b) of the line

Equation of a line in the slope y-intercept form:

y = mx + b

y = 8x + 120

C) The y-intercept indicates the number of products produced monthly without employees.

The slope indicates how much the production increase with a new employee.