A student is looking at the relationship between the number of workers in a factory and the number of units produced daily. The table shows the data:

Number of workers (X) 1, 2, 3, 4, 5, 6, 7, 8, 9.
Number of units (Y) 7, 11, 12, 16, 17, 24, 23, 26, 32.

Based on the table, answer the following questions:

Part A: Describe 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 an equation for a line of fit or the line of best fit for the data. Show all work. (3 points)

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

C. slope: increasing by 1 worker increases output about 2.9 units; intercept: small numbers of workers have greater productivity than larger numbers.

Step-by-step explanation:

You want a description of the correlation between workers and units produced, based on the given table. You also want an equation for a best-fit line, and an interpretation of the slope and intercept.

A. Correlation

A calculator tells you the correlation coefficient is about 0.983. This is a strong positive correlation, meaning factory output will increase with increasing numbers of workers.

B. Equation

A calculator tells you the line of best fit is approximately ...

Y = 2.92X +4.08

C. Slope and Intercept

The positive y-intercept suggests that factory output will be 4 units even if there are 0 workers. We suspect that is unlikely, but it means the first worker is substantially more productive than the next few workers.

The slope of about 3 means each additional worker adds about 3 units to the total factory output.

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Additional comment

We note that output actually declines when worker 7 is added. On the other hand, adding worker 6 increased output by as much as adding worker 1, an increase more than double that of the average worker.