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)

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.

Part A: Yes there is a correlation because every new month there are 10 new employees, and every 10 new employees, 80 new products are produced monthly. This shows a linear function throughout the table because the data is increasing at the same amount every month.

Part B: A linear function uses the function (y = mx + b). To find m, you need to use the equation (y2 -y1/x2 -x1), like so, (200-120/1-0) = (80,10) = (8). To find out what b equals in the equation (y = mx + b), I need to put in what I already know, which is (y = 8x + b). Then I’m going to substitute the y and x for numbers from the data to find out what b is (don’t worry, I am not going to keep the numbers there, this is only to find out what b is.) I’ll go with the numbers (10, 200), (200 = 8 times 10 + b) = (200 = 80 + b) next step is to get ride of the 80, so that the b is alone, (200 - 80 = b) = (120 = b). You can chose another pair of (x,y) to check my number. The finale function is, (y = 8x + 120).

Part C: The y- Intercept indicates the number of products produces monthly without employees and the slope indicates the increasing value of products going up monthly for every new employee.

Step-by-step explanation:

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