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 25 50 75 100 125 150 175 200 Number of products (y) 10 160 310 460 610 760 910 1060 1210 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?

Answer 1

Answer:

A)there is a strong positive correlation

B)A function that best fits the data is $\widehat{y}=6x+10$

C)Slope indicates the rate of change of Number of products per employee

y intercept indicates number of products when number of employees are 0

Step-by-step explanation:

Number of employees (x) 0  25  50  75  100  125  150  175  200

Number of products (y)   10 160 310 460 610 760 910 1060 1210

Part A: Is there any correlation between the number of employees in the plant and the number of products produced yearly?

Mean of x values = $\frac{0+25 + 50 + 75 + 100 + 125 + 150 + 175 + 200}{9}=900$

Mean of y values = $\frac{10+160+ 310+ 460+ 610+ 760+ 910+ 1060+ 1210}{9} =610$

$\sum(x-\bar{x})^2= 37500$

$\sum(y - \bar{y})^2 = 1350000$

N =No. of observations= 9

$\sum(x - \bar{x})(y-\bar{y}) = 225000$

R Calculation

$r = \frac{\sum((x-\bar{x})(y - \bar{y}))}{\sqrt{\sum(x - \bar{x})^2(y-\bar{y})^2}}$

$r=\frac{225000}{\sqrt{(37500)(1350000)}}\\r= 1$

So, there is a strong positive correlation

B: Write a function that best fits the data.

Regression Equation = ŷ = bx + a

$b = \frac{225000}{37500} = 6\\a = \bar{y} -b \bar{x} = 610 - (6 \times 100) = 10\\ \widehat{y}= 6x + 10$

So, a function that best fits the data is $\widehat{y}=6x+10$

C)What does the slope and y-intercept of the plot indicate?

Slope indicates the rate of change of Number of products per employee

y-intercept indicates the y-coordinate of a point where a line, curve, or surface intersects the y-axis.

So, y intercept indicates number of products when number of employees are 0 .