# Creating a Market Pay Line Using Regression Analysis

The source for the following article is “Designing a Pay Structure” written by Lisa A. Burke and published by Society for Human Resource Management.

Step 1 We used job analysis to create job descriptions for our benchmark jobs.

Step 2 We created an internal hierarchy of jobs (i.e., an internal job structure) by using the point method to evaluate each of our benchmark jobs.

Step 3 Let us assume that we are working only on three job families (HR, Office Support, and Operations) After our pay strategy was determined for the three job families, we analyzed the pay survey information gathered from competitors in our relevant labor market.

Step 4 We now have internal job point data and externally gathered weighted average base pay for each benchmark job. We can now proceed to co-relate the internal and external data to create our market pay line.

One way to do this is through a simple regression using Microsoft Excel to create a market pay line. Enter the job evaluation points (on the X axis) and weighted average base pay rates (on the Y axis) for each benchmark job and generate the regression results.

Regression creates a “line of best fit” by co-relating the job evaluation points on the X axis and the external salary data on the Y axis. The resulting regression line can then be use to predict the base pay (on the Y axis) for a specific number of job evaluation points (on the X axis). The equation for the simple regression line can be represented as: y=mx+b; in which
y is the predicted base pay;
m is the slope of the line
x is the job evaluation points
b is the y-intercept

Step 5 Identify the slope and y-intercept and write the equation for the market pay line.
For example, if the regression results show that m = 400 and b is -20000, then the equation is y=400(x) – 20000 and the predicted pay rate for a job assigned 100 points would be y= 400(100)-20000, or \$20,000.

Just to recap on the basic concepts

Linear regression is used to explore the connection between a single independent variable/covariate/predictor that act on a single dependent variable/outcome.

The R value is a measure of correlation between the predicted and observed values of the independent variable.

One quantity people often report when fitting linear regression models is the R squared value (R2) or coefficient of determination. This measures what proportion of the variation in the outcome Y can be explained by the covariate/predictor X. You can think of R2 as the fraction of the total variance of Y that is explained by the model (equation).

Simply said,it tells you how many points fall on the regression line, for example, 80% means that 80% of the variation of y-values around the mean is explained by the x-values. In other words, 80% of the values fit the model.

For simple linear regression, R2 is the same as the correlation, R, squared.

Multiple regression is used to explore the connection between multiple independent variables that act on a single dependent variable.

Similar to R2 in simple linear regression, R2 can be calculated for multiple regression (also called multiple R2). It is an indicator on how well the x-variables can be used to predict the value of the y-variable. In other words, R2 indicates the strength of the regression equation which is used to predict the value of the y-variable. R2 is also known as the multiple correlation coefficient.

If R squared is close to 1, it means that the covariates can jointly explain the variation in the outcome Y. This means Y can be accurately predicted (in some sense) using the covariates. Conversely, a low R squared means Y is poorly predicted by the covariates.

Step 6 The multiple R squared will indicate the amount of variance explained in Y (market pay) by X (job evaluation points). This shows how good the regression line fits the data. It should be .95 or higher. This .95 guidepost for the amount of variance explained is a general guideline (see Milkovich, G., & Newman, J. (2008) Compensation, McGrawHill Irwin).

If R squared is significantly lower than this, there may be problems stemming from the job evaluation step. Alternatively, there may be errors in the weighted average calculations.

A multiple R of .98 would produce an R squared of .96 [.98*.98 = .96.], indicating that X (i.e., your job evaluation points) explains about 96% of the variance in Y (i.e., the market pay).

Step 7 Use the regression output (the slope and y-intercept) to calculate the predicted market pay rate (using Excel) for each benchmark job.

For example, with a slope of 250 and y-intercept of -1200, the 120 points assigned to the Front Desk Receptionist job would translate into a predicted base pay rate of \$28,800. y=(250*120) –1200 = 28800