Question

A manager is assessing the correlation between the number of employees in a plant and the number of products produced yearly. The table shows the data:


Number of employees
(x) 0 50 100 150 200 250 300 350 400
Number of products
(y) 100 1,100 2,100 3,100 4,100 5,100 6,100 7,100 8,100


Part A: Is there any correlation between the number of employees in the plant and the number of products produced yearly? Justify your answer. (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

Answer is attached!
Hope this helps :)

Answer 2

Given:

employees (x)  0      50     100     150   200    250     300      350    400

products     (y) 100 1,100 2,100  3,100  4,100  5,100  6,100  7,100  8,100

part A:

There is a positive correlation. with increase in employees, there is increase in products.

part B:

find slope:

$\sf \frac{y1-y}{x1-x}$

$\sf \frac{1100-100}{50-0}$

$\sf \frac{1000}{50}$

$\sf 20$

equation:

$\sf y - y1 = m ( x - x1 )$

$\sf y - 100 = 20 ( x - 0 )$

$y = 20 x +100$

part C:

slope: 20 - this indicates the unit rate of products per employees

when y-intercept, x will be 0 - this indicates the initial products and employees.