Space Toy Co. produced Proportional Value job rates using the free-hand method, as shown on the previous page, but chose to verify these results and construct a job rate line by using a computer and a statistical method called regression analysis.
Regression vs Free-Hand
When the Proportional Value line was drawn free-hand, the line was fit in place visually. A clear ruler was positioned on top of the scattergram, with the straight edge passing through the pivot point. The ruler was moved until the straight edge fit the data most closely. This required that the line be adjusted until one was drawn that fit the points on the scattergram.
Regression analysis is the mathematical way of accurately finding the line which best fits the points on the graph. Regression analysis calculates a line that produces the smallest sum of distances of points to the line. The calculations can be done using a computer program or a calculator with the regression function. Unlike drawing a line free-hand, this method does not entail a trial-and-error process.
What the Regression Output Numbers Mean
When you do regression on the computer, you will generate a series of numbers, called "Regression Output", not all of which you will need. The numbers you should familiarize yourself with are the constant (or intercept), the x co-efficient (or slope), and the R-squared.
The constant predicts what your organization would pay a job worth zero points. Imagine this as a base rate; every job is paid at least the constant. Then the x co-efficient identifies how much above the constant the jobs would be paid for each point scored. These are the two numbers you need to predict the pay equity job rate for each female job class using the following equation:
- pay equity job rate = constant + (slope x job value)
The other important number to consider is the R-squared. The R-squared indicates how closely, overall, all the points on the scattergram fit to the regression line. An R-squared of 1.0 indicates a perfect fit - or that all job rates are perfectly related to job value. This will almost never be the case. An R-squared of .90 indicates a very good fit. An R-squared at or below .5 suggests there may be a problem establishing a pattern between job value and job rate.
Pay Attention to the Numbers
When you get your regression output, watch out for these potential problems:
Was your constant near or below zero?
A negative constant suggests that a job worth zero points is worth less than zero dollars. Where a negative constant is generated, consider whether the representative group of male job classes includes highly valued jobs with very high job rates. If so, it may be possible that these should not be included in the representative group. These could be a separate representative group of male jobs, representative or closer in value to female job classes at the managerial or professional levels. If the predicted job rates are well below the current rates for job classes near the lower end of the value scales, check to ensure that you have a truly representative group.
Was your R-squared below .75?
While it is difficult to identify a cut-off point below which an R-squared may be problematic, it is best to strive for a line which most closely represents how jobs are paid for their value. If you have a low R-squared, you might try to remove a few "outliers" from the line. Outliers are jobs that appear to fall outside the pattern of the majority.
Create a Line using your Computer
Space Toy Co. followed a series of steps to produce Proportional Value job rates using regression. Each step is summarized on the next page. Please refer to your computer's "Help" section on regression analysis if you need further clarification on using this program.