Answer:
Part A)
- The observation from the the table indicates that if the value of variable [tex]x[/tex] increases, the value of variable [tex]y[/tex] also increases.
Part B)
- [tex]y=6x+10[/tex] is the function that bets fits the data.
Part C)
- The slope defines that a single worker is able to produces 6 units.Thus, for a given number of workers x, the units produced would be [tex]6x[/tex].
- The y-intercept defines that for the total number of units produced [tex]y[/tex] by [tex]x[/tex] number of workers, [tex]10[/tex] units would be added.
Step-by-step explanation:
Part A)
We know that
- Negative correlation means when one variable decreases, then the other variable also decreases.
- Positive correlation means when one variable increases, then the other variable also increases.
Given the table data
Number of employees (x)
(x) 0 25 50 75 100 125 150 175 200
Number of Products (y)
(y) 10 160 310 460 610 760 910 1060 1210
The observation from the the table indicates that if the value of variable [tex]x[/tex] increases, the value of variable [tex]y[/tex] also increases.
Thus, the two variables i.e. Number of employees (x) and Number of Products (y) will have positive correlation.
Please check the attached graph in figure a to determine that the positive correlation as the value of variable [tex]x[/tex] increases when the value of variable [tex]y[/tex] also increases.
Part B)
Given the table data
Number of employees (x)
(x) 0 25 50 75 100 125 150 175 200
Number of Products (y)
(y) 10 160 310 460 610 760 910 1060 1210
As we know that the point slope form
[tex]y=mx+b[/tex]
where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.
Lets take the point (0, 10) and point (200, 1210)
As
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
[tex]m=\frac{1210-10}{200-0}[/tex]
[tex]m=\frac{1200}{200}[/tex]
[tex]m=6[/tex]
As
[tex]y-y_{1} = m(x-x_{1})[/tex]
[tex]m = \frac{y-y_{1}}{x-x_{1}}[/tex]
Taking any point, let say (25, 160), and putting in
[tex]m = \frac{y-y_{1}}{x-x_{1}}[/tex]
[tex]6\:=\:\frac{y-160}{x-25}[/tex]
[tex]y=6x+10[/tex]
Hence, [tex]y=6x+10[/tex] is the function that bets fits the data.
Part C)
As we have determined the equation
[tex]y=6x+10[/tex]
Here,
- Slope = m = 6
- y-intercept = 10
The slope defines that a single worker is able to produces 6 units.Thus, for a given number of workers x, the units produced would be [tex]6x[/tex].
The y-intercept defines that for the total number of units produced [tex]y[/tex] by [tex]x[/tex] number of workers, [tex]10[/tex] units would be added.
Keywords: slope, function, linear function, correlation
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