Answer:
A)there is a strong positive correlation
B)A function that best fits the data is ![\widehat{y}=6x+10](https://tex.z-dn.net/?f=%5Cwidehat%7By%7D%3D6x%2B10)
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](https://tex.z-dn.net/?f=%5Cfrac%7B0%2B25%20%2B%2050%20%2B%2075%20%2B%20100%20%2B%20%20125%20%2B%20150%20%2B%20175%20%2B%20200%7D%7B9%7D%3D900)
Mean of y values = ![\frac{10+160+ 310+ 460+ 610+ 760+ 910+ 1060+ 1210}{9} =610](https://tex.z-dn.net/?f=%5Cfrac%7B10%2B160%2B%20310%2B%20460%2B%20610%2B%20760%2B%20910%2B%201060%2B%201210%7D%7B9%7D%20%3D610)
![\sum(x-\bar{x})^2= 37500](https://tex.z-dn.net/?f=%5Csum%28x-%5Cbar%7Bx%7D%29%5E2%3D%2037500)
![\sum(y - \bar{y})^2 = 1350000](https://tex.z-dn.net/?f=%5Csum%28y%20-%20%5Cbar%7By%7D%29%5E2%20%3D%201350000)
N =No. of observations= 9
![\sum(x - \bar{x})(y-\bar{y}) = 225000](https://tex.z-dn.net/?f=%5Csum%28x%20-%20%5Cbar%7Bx%7D%29%28y-%5Cbar%7By%7D%29%20%3D%20225000)
R Calculation
![r = \frac{\sum((x-\bar{x})(y - \bar{y}))}{\sqrt{\sum(x - \bar{x})^2(y-\bar{y})^2}}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B%5Csum%28%28x-%5Cbar%7Bx%7D%29%28y%20-%20%5Cbar%7By%7D%29%29%7D%7B%5Csqrt%7B%5Csum%28x%20-%20%5Cbar%7Bx%7D%29%5E2%28y-%5Cbar%7By%7D%29%5E2%7D%7D)
![r=\frac{225000}{\sqrt{(37500)(1350000)}}\\r= 1](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B225000%7D%7B%5Csqrt%7B%2837500%29%281350000%29%7D%7D%5C%5Cr%3D%201)
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](https://tex.z-dn.net/?f=b%20%3D%20%5Cfrac%7B225000%7D%7B37500%7D%20%3D%206%5C%5Ca%20%3D%20%5Cbar%7By%7D%20-b%20%5Cbar%7Bx%7D%20%3D%20610%20-%20%286%20%5Ctimes%20100%29%20%3D%2010%5C%5C%20%5Cwidehat%7By%7D%3D%206x%20%2B%2010)
So, a function that best fits the data is ![\widehat{y}=6x+10](https://tex.z-dn.net/?f=%5Cwidehat%7By%7D%3D6x%2B10)
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 .