Question

A manager is assessing the correlation between the number of employees in a plant and the number of products produced yearly. The tableshows the data:Number of employees0 50100 150 200 250 300 350 400(x)Number of products100 1.1002,1003,100 4,100 5,100 6,1007,100 8,100(y)Part A: Is there any correlation between the number of employees in the plant and the number of products produced yearly? Justify youranswer. (4 points)Part B: Write a function that best fits the data. (3 points)Part C: What does the slope and y-intercept of the plot indicate? (3 points)

Answer 1

Step-by-step explanation:

Part A

Looking at the table, as the number of employees is increasing, the number of products is also increasing. This means that there is a correlation between the number of employees and number of products produced. Thus, it is Yes

Part B

The table shows that the function is linear. The equation of a line in the slope intercept form is expressed aa

s

y = mx + c

where

m is the slope

c is the y intercept

We would find the slope by applying the formula,

m = (y2 - y1)/(x2 - x1)

From the table,

when x1 = 0, y1 = 100

when x2 = 50, y2 = 1100

m = (1100 - 100)/(50 - 0) = 1000/50 = 20

The y intercept, c is the value of y when x = 0

From the table,

c = 100

Thus, the function that fits the data is

y = 20x + 100

Part C

The slope indicates the number of products produced per employee

The y intercept represents the number of products produced when there were zero employees or before the employees started working.