For an analysis of the salaries of your company, you plot the salaries of all employees against the number of years they have worked for the company. You find that plotting the base-10 logarithm of salary makes the plot much straighter. A part-time shipping clerk, who has worked at the company for one year earns $12 comma 000. A manager earns $120 comma 000 after 20 years with the firm. The CEO, who founded the company 40 years ago, receives $1 comma 500 comma 000. What are the values you will plot? Will the plot of these three points be straight enough?

1. That values that you must plot are:

2. Yes, the plot of those three points is straight enough.

Explanation:

A. What are the values you will plot?

The x-ccordinate of your plot is still the number of years the exmployees have worked for the company.

The y-coordinate of your plot is the the base-10 logarithm of  the salary.

Therefore:

1) A part-time shipping clerk: 1 year, $12,000

           ⇒    

2) A manager: 20 years, $120,000

  ⇒    

3) The CEO: 40 years ago, $1,500,000

  ⇒    

Summarizing, the points to plot are:

B. Will the plot of these three points be straight enough?

To find whether the plot is straight enoguh, you may either plot them, make a regression, or, since they are only three points, you can whether the change of rate of the points is constant.

       r = rise/run = Δy / Δx = (5.08 - 4.08) / (20 - 1) =1.00/19 ≈ 0.05

       r = rise/run = Δy / Δx = (6.18 - 5.08) / (20 - 1) = 0.05

Since both rate of changes are equal (or reasonably equal) the plot is  straight enough.

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