Amanager 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)

we will first plot all x,y points on graph as shown in attachment.

(a) as you can see in attachment we get straight line so we can say yes number of employess are correlated to number of products produced monthly. they are linearly correlated by linear function

(b) as its straight line so it has to be linear function

to write linear function equation we will select any two random points on graph here. lets say (0,120) and (10,200)

so first find slope using slope formula

for two points given and

so for point (0,120) and (10,200) we will have slope as

equation of line is given by

so lets plug 8 in m place , 0 in place and 120 in place in formula

y - 120 = 8(x - 0)

y - 120 = 8 (x)

now solve for y and get y by itself

y - 120 = 8x

y - 120 + 120 = 8x + 120

y = 8x +120

so thats the equation of function that best fits the data

(c) slope = 8 indicates rate of increase or how fast is the number of products produced monthly is changing with number of employees.

y intercept is point where line cuts y axis which is at (0,120). so that means for 0 number of employees (x) we have number of products produced monthly(y) as 120. so intially there were 120 products