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)

step-by-step explanation:

we see from the table that for increase of 10 units in x, there is an increase of 80 units in y

hence slope of line is 8

when x=0, y =120 that is c =120

hence regression line has equation

y = 8x+120

since all points lie on the regression line, the linear relationship is perfect and hence correlation is strong.

so correlation is +1 since there is a positive increase in y.

parta:   yes,   there is a perfect linear positive strong correlation between the number of employees in the plant and the number of products produced monthly

(the slope is positive 8)

part b:   y = 8x+120

part c:   slope indicates the rate of change of y for a unit change in x.

y intercept is the y value for x=0

part a. yes there is a correlation between the number of employees and the number of products produced. in fact, the correlation is linear relationship. we can see that for every 10 increase in employee, there is a consistent increase of 80 products therefore the correlation is linear.

part b. since the relationship is linear, therefore the function takes the form:

y = m x + b

where m is the slope of the line and b is the y-intercept of the line. the value of b is equal to the value of y when x = 0, therefore:

b = 120

calculating for m using two data pairs:

m = (y2 – y1) / (x2 – x1)

m = (200 -120) / (10 – 0)

m = 8

therefore the function is:

y = 8 x + 120

part c. the slope indicates the increase in y per value of x. since slope is 8 therefore there is an increase in 8 products per employee. while the y-intercept indicates the initial value of y, when x = 0.

i hope this is what you were looking for.

see attached graph