Ordinary Least Squares Regression of Salary Survey Data

Tuesday, January 19, 2010

Ordinary Least Squares Regression(OLS) is commonly used to analyze the relationship between market wage rates and the grades or job evaluation points associated with surveyed positions. The object is to calculate the new range mid-points from the survey market wage rates. Market rates are represented by the weighted/non-weighted Median or Mean market rates. If available a weighted data value is more preferable than un-weighed data. The Median is preferable over the Mean since the Median, which is also the 50th percentile, is less susceptible to extreme data values that would skew the Mean, thus making the Median a better representation of the “mid-points” of the market rates.

In most common salary structure design and analysis the analyst is working with two variables, the market rates and the grades/points of the surveyed positions. The Ordinary Least Squares Regression formula (y = mx + b) converts the values of those variables into a set of fitted set of points representing the market rate mid-points. Once these points are known, it is a simple process to calculate Maximums and Minimums, by example:

In the above example using pay grades, the organization has a 10-grade structure for some portion of its workforce. The organization has obtained market rates from a salary survey or other process and used Ordinary Least Squares Regression to project the new salary range mid-points. Applying Ordinary Least Squares Regression (most spreadsheet have preprogrammed functions for this) the following values are calculated for the slope(m), $831 and the intercept point(b), $24,969.

Substituting the values for slope and intercept into the OLS formula for Grade # 1, we have:

(y = mx + b)
y = $831*1+$24,969 ..... Since this is for Grade 1, x=1.
y = $25,800 ................. For Grade 1, we have a Projected Mid-Point of $25,800

We repeat the process for Grade # 2:

(y = mx + b)
y = $831*2+$24,969 ..... Since this is for Grade 2, x=2.
y = $26,630 ................. For Grade 2, we have a Projected Mid-Point of $26,630

We repeat the process for Grade # 3:

(y = mx + b)
y = $831*3+$24,969 ..... Since this is for Grade 3, x=3.
y = $27,461 ................. For Grade 3, we have a Projected Mid-Point of $27,461

We repeat the process for Grade #’s 4, 5, 6, …, 10, substituting the next grade into the formula and calculating the projected mid-point. The power of OLS is that it “smooths out” variations in the market data to produce a “best fit” line along a set of points. The range mid-points corresponds to the projected mid-point.