A nonprofit home healthcare agency has asked “a consultant” whether its CEO is fairly paid relative to the marketplace for similar agencies. The Agency has supplied a database to the consultant, who also has his own survey database of CEO pay.
This case will demonstrate how regression data can be used to answer this question. David Wudyka, SPHR, MBA, BSIE, is the Managing Principal and founder of Westminster Associates in Wrentham, Massachusetts. His tips came during a recent webinar sponsored by BLR®.
In this case, the CEO’s rate is $79.50 per hour (or $165,360 per year). The Agency’s revenue is $25M. Is the CEO fairly paid? The survey of nonprofit home health- care agency pay levels shows the pay levels in the table below.
This case will demonstrate how regression data can be used to answer this question.
The independent variable is “Revenue”; the dependent variable is “CEO base pay.”
First (to Be Safe)
Be sure that you array the data from high to low for your independent variable (and, of course, be sure to link the dependent variable values to the associated independent variable values when you sort the data).
Double-check that your statistical software accurately calculates regression data if you don’t sort your data!
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Next, Set Up Excel
If you have not already done so, in Excel 10.0, download the analysis tool pack, the “analysis toolpack”.
Go to file → options→add-ins→highlight “analysis toolpack”→ “go”→ “check” box for toolpack in next dialog box that appears → “OK.”
To access the tool pack, click “data” in menu ribbon at top. “Data analysis” will be on your far right in menu line at top.
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To Perform Regression Analysis
Go to “data analysis” →click “regression” →OK
Specify the following:
- Input ranges: x (i.v.) and y (d.v.) variables.
- Set confidence level: 95%.
- Select output range (pick a cell in the spreadsheet).
- Click “OK”; the output will appear.
Reading the Analysis Output:
Our results are:
- r² = .9075 = .9 (Good! It means that 90% of the variation in the dependent variable of CEO Base Pay can be “explained” by the independent
- The “y-intercept” value (“b” in straight-line equation) = 39.378
- The “coefficient” value is 1.47417E-06. This translates to .00000147417 from scientific notation.
variable of Revenue level.) A very strongly correlated result. In studies with a good quality data base, typical r2 value is around .7.
Sample Output Calculation
At $25M Revenue (your company’s revenue), the calculation is as follows:
Constant $39.38 + .00000147417 x 25,000,000
$39.38 + $36.85 = $76.23 (annualized = $158,558)
Is the CEO appropriately paid? Her rate is $79.50. Therefore, it appears that her base pay rate is “in the market.” What’s “in the market”? Use a tolerance range of +/- 5 percent to 10 percent.
What if her performance is lagging? You probably would not make an adjustment; however, we don’t know about the performance levels of all the others in the data sample.
Conclusion
Statistics are “abstractions” of data that help us to understand the nature of the data better, says Wudyka. This can help us to make practical decisions about employees and the workplace in many ways. However, be sure to interpret data carefully. Don’t “read too much into” the data. Use statistics as an important tool that complements your personal observations in your company!
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