Question

A student is assessing the correlation between the number of workers in a factory and the number of units produced daily. The table below shows the data:
Number of workers
(x) 0 10 20 30 40 50 60 70 80 90
Number of units
(y) 2 52 102 152 202 252 302 352 402 452

Part A: Is there any correlation between the number of workers in a factory and the number of units produced daily? Justify your answer. (4 points)

Part B: Write a function which best fits the data. (3 points)

Part C: What does the slope and y-intercept of the plot indicate? (3 points)

Answer 1

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 y = 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.

How can the existence of a correlation and the best fit function for the data be found?

Part A:

The correlation is the relationship between variables based on statistical data.

From the given table, the difference between consecutive terms of the x 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, x, and the number of units produced, y.

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 x and y-values is a linear function, which can be found as follows;

Slope of the equation, m = ∆y/∆x

Which gives;

m = 50/10 = 5

y - 2 = 5•(x - 0)

The function that best fits the data is therefore;

• y = 5•x + 2

Part C:

The slope of the function is the coefficient of the variable x in the equation, y = 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:

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