Regression
Traditionally, statistical techniques, including regression analysis, have been used to define required staffing levels. With these techniques, statistical analyses are used to define the historical relationships between staffing levels and other variables (e.g., developing an equation that relates actual sales volume achieved to the number of sales staff employed). The use of regression requires historical data on both the independent variable(s) (e.g., sales, number of products produced, number of customers served) and the dependent variable (usually staffing levels or full-time equivalents). There are several types of regression analysis, including the following:
Simple, or single. This technique defines a straight-line relationship between one independent variable and one dependent variable (e.g., relating sales to the number of sales staff).
Multiple. This technique defines a straight-line relationship among two or more independent variables and the dependent variable (e.g., relating both total sales and the number of accounts served to the number of sales staff).
Curvilinear. This technique defines nonlinear relationships between independent and dependent variables. Because of its complexity, it is less commonly used (and won’t be discussed here).
To develop a single regression model, create a table that captures actual historical data for each variable. Each row of the table should include the value of the independent variable (e.g., actual total sales) at a particular point in time and the value of the corresponding dependent variable (e.g., the number of staff actually on board and supporting that work) at that same point in time. An eight-quarter model would thus include eight rows or data points. Here is what a simple one might look like:
| Quarter | Total Sales ($000) | Number of Sales Staff |
|---|---|---|
| 1Q 2006 | 2,000 | 5 |
| 2Q 2006 | 2,125 | 5 |
| 3Q 2006 | 2,403 | 6 |
| 4Q 2006 | 2,599 | 6 |
| 1Q 2007 | 2,680 | 6 |
| 2Q 2007 | 2,598 | 7 |
| 3Q 2007 | 2,821 | 7 |
| 4Q 2007 | 3,011 | 8 |
Next, enter these data into a program that includes a regression routine. Most spreadsheet programs usually include such routines, and virtually all statistical packages include a regression capability as well. Many business-oriented calculators also have simple regression capability.
The output of the analysis is an equation that describes the best fit between your independent and dependent variables. In the case of single regression, the equation is of the form:
y = ax + b
where y is the dependent variable (e.g., staffing levels), x is the independent variable (e.g., sales), and a and b are values determined by a regression analysis. A regression analysis of the simple eight-quarter model given here produces this equation:
Number of Sales Staff = 0.0027896 × Sales (in thousands) + 0.8067036
To use this equation to forecast staffing levels, you simply obtain projections for the future values of the independent variables you have used (e.g., get projected sales levels from sales forecasts), enter these in the equation you have created, and calculate the required staffing level. In this simple example, if expected sales for the coming quarter were projected to be $3,000,000, then the expected number of sales staff needed to support that level of activity would be 7.56 (i.e., 0.0027896 × 3,000 – 0.8067036).
Multiple regression is similar, but it includes more than one independent variable. If there are two independent variables, the regression equation is of the form:
s = ax + by + z
where s is the dependent variable (e.g., staffing levels), x and y are the independent variables (e.g., total sales and number of accounts), and a, b, and z are values determined by the regression analysis. Again, spreadsheet programs can often be used to produce multiple regression analyses, and most statistical packages include multiple regression routines as well. To develop a multiple regression model, again create a table that captures actual historical data for all variables. Each row of the table should include the value of each independent variable (e.g., actual total sales and actual number of accounts) at a particular point in time and the value of the corresponding dependent variable (e.g., the number of staff actually on board and supporting that work) at the same point in time. A 12-quarter model would thus include 12 rows. To use a multiple regression equation to forecast staffing levels, simply obtain projections for the independent variables you have used, enter these in the equation you have created, and calculate the staffing that will be needed.
Suppose, for example, that your equation was in this form:
Number of Sales Staff = [0.100 × Sales (in millions)] + (0.01 × Number of Accounts) + 2
In this example, if expected sales were $100 million and the number of accounts was 200, then the expected number of sales staff needed to support that level of activity would be 14:
Number of Sales Staff = (0.100 × 100) + (0.01 × 200) + 2 = 14
All regression techniques have limitations. First, they work only in situations in which “the past is prologue”—that is, those situations in which the expected work and conditions in the future resemble those of the recent past. If you think the future will differ significantly from the past, don’t use this approach. A second caution is also in order: Technically speaking, regression relationships (and thus regression models) are valid only within the range of the data that were used to construct the model in the first place. Regression equations should be used to forecast required staffing levels only if the sales projections fall within the range of sales that has actually been observed in the past. For example, suppose you built a regression model that related actual sales for a quarter to the number of sales staff that supported that volume. If the lowest level of quarterly sales actually observed was $20 million and the highest was $40 million, the model would be valid only for this particular range of quarterly sales. It should not be used to forecast the number of staff that would be needed to support anticipated sales of $50 million (or $10 million, for that matter).
Regression is best applied where there are direct relationships between the amount of work that is done and the number of staff doing that work. Further, you must be able to define the work or output in quantifiable terms. The technique should also be applied primarily to job categories that have relatively large numbers of staff that are doing substantially similar work.
There is another situation in which regression works quite well. Instead of building a historical database for a given unit, you can use the process to analyze staffing across units at a given point in time. Suppose that your organization has branch offices of various sizes that are handling different workloads. Regression can be used to define the relationship between staffing and workload across branches or locations. Once the regression equation has been developed, it can be used to define the “ideal” staffing level for any given workload for any branch.