The number of units produced increases from 2 to 452 as the number of factory workers increases from 0 to 90, which gives;
Part A:
- Yes there is a strong positive correlation
Part B:
- The function is <em>y</em> = 5•x + 2
Part C:
- The slope indicates the number of units produced by each worker daily
- The y-intercept indicates that two units can be produced without workers.
<h3>How can the existence of a correlation and the best fit function for the data be found?</h3>
Part A:
The correlation is the relationship between variables based on statistical data.
From the given table, the difference between consecutive terms of the <em>x </em>and y-values are constant, therefore as the x-values increases, the corresponding y-value increases.
Change in x-values, ∆x = 10 - 0 = 20 - 10 = 30 - 20 = 10
Change in y-values, ∆y = 52 - 2 = 102 - 52 = 152 - 102 = 50
Therefore;
- There is a strong positive correlation between the number of workers, <em>x</em>, and the number of units produced, <em>y</em>.
Part B:
Given that the rate of change of the x-values is constant, and the rate of change of the y-values is a constant, the function relating the <em>x </em>and y-values is a linear function, which can be found as follows;
Slope of the equation, <em>m </em>= ∆y/∆x
Which gives;
m = 50/10 = 5
y - 2 = 5•(x - 0)
The function that best fits the data is therefore;
Part C:
The slope of the function is the coefficient of the variable <em>x </em>in the equation, <em>y </em>= m•x + c
- The slope of the plot, 5, indicates that each worker produces 5 units daily
The y-intercept of the function is the value of the constant term, c, in the equation, y = m•x + c
- The y-intercept of the linear equation, y = 5•x + 2, which is 2, indicates that the initial number of units of products at the factory before workers arrive is 2.
Learn more about finding relationship between variables here:
brainly.com/question/4219149
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