Answer :
Answer:
A) Positive correlation
[tex]\textsf{B)}\quad y=\dfrac{35}{12}x+\dfrac{49}{12}\quad \textsf{or}\quad y=2.917x + 4.083[/tex]
C) See below
Step-by-step explanation:
Part A
Correlation is a statistical measure that shows how two variables are related. It can be positive (both increase or decrease together), negative (one increases as the other decreases), or no correlation (no apparent relationship).
To determine the correlation between the number of workers and the number of units produced daily, we can examine the trend in the data. If we plot the data points, we can see that they are close to forming a straight line with a positive slope. This suggests a positive correlation between the two variables. So, when the number of workers increases, we observe an increase in the number of units produced daily.
[tex]\dotfill[/tex]
Part B
To find the equation for the line of best fit, we can use linear regression.
After entering the data from the given table into a statistical calculator we get:
[tex]a = 2.91666...=\dfrac{35}{12}\\\\\\b = 4.08333...=\dfrac{49}{12}[/tex]
To determine the regression equation, substitute the found values of a and b into the regression line formula, y = ax + b.
So, the equation for the line of best fit is:
[tex]y=\dfrac{35}{12}x+\dfrac{49}{12}[/tex]
If the coefficients should be decimals, then the equation is:
[tex]y=2.917x + 4.083[/tex]
[tex]\dotfill[/tex]
Part C
The slope of the line indicates that for each additional worker, the number of units produced daily increases by approximately 2.92 units. This suggests that an increase in labor leads to an increase in production.
The y-intercept indicates that the expected number of units produced when there are no workers in the factory is 4.08 units.
