Pay Equity Commission :: The Space Toy Co. Case Study :: How to Calculate the Regression Line Equation Manually

If you can't use the interactive forms on the previous page (JavaScript may be disabled on your computer), you can still create a wage line manually by following the steps outlined on this page.

To help you with your calculations, we've provided two examples of completed data tables from a fictitious organization (Tables 1 and 2 on this page).

Three blank tables are also provided for your manual calculations. You can print and fill out these forms manually:

Table # 1 shows the results of an organization's regression calculations. Some of the data in this table will be used to clarify the steps necessary to produce PV job rates.

Table 1
Example of a Manual Regression Calculation
Male Job Classes	Job Value (X)	Job Rate $ (Y)	Deviation from Average Job Value (X-XM)	Deviation from Average Job Rate $ (Y-YM)	Square of (X-XM)	Square of (Y-YM)	Product of (X-XM)(Y-YM)
	A	B	C	D	E	F	G
Sales Manager	795	32.96	133.67	7.06	17868	49.84	943.71
Marketing Manager	770	29.88	108.67	3.98	11809	15.84	432.51
Controller	762	28.35	100.67	2.45	10134	6.00	246.64
Warehouse Manager	700	25.81	38.67	-0.09	1495	0.01	-3.48
Market Analyst	660	25.30	-1.33	-0.60	2	0.36	0.80
Sales Representative	630	26.83	-31.33	0.93	982	0.86	-29.14
Accountant	610	24.00	-51.33	-1.90	2635	3.61	97.53
Programmer	555	21.00	-106.33	-4.90	11306	24.01	521.02
Shipper/ Receiver	470	19.00	-191.33	-6.90	36607	47.61	1320.18
Sum	5952	$233.13	*0.03	*$0.03	92838	148.14	3529.77
Mean (Average)	661.33	$25.90

Step 1:
Prepare data for Table # 1 (Manual Regression Calculation)

Print the blank Table 1-a (looks exactly like Table # 1 above, but with empty cells) and start entering your own data using the step-by-step instructions and examples below.

Enter the representative male job classes in the Male Job Classes column, and the job values and job rates in Columns A and B.

Add the data in Column A and calculate the mean, or average. Do the same for Column B.

Example from Table 1:
Total of Column A: 5952
Average of Column A: 5952 ÷ 9 = 661.33
Total of Column B: $233.13
Average of Column B: $233.13 ÷ 9 = $25.90

Substract the average job value from Column A from the job value of each job class.

Example from Table 1:
Sales Manager
Job value - average job value = Column C
795 - 661.33 = 133.67

This number (133.67) is recorded beside the job class of Sales Manager in Column C. When you add up Column C, the sum will equal zero (0), if your calculations are correct. (Variances from zero may exist due to rounding).

Substract the average job rate from Column B from the job rate of each job class.

Example from Table 1:
Sales Manager
Job rate - average job rate = Column D
$32.96 - $25.90 = $7.06

This number ($7.06) is recorded beside the job class of Sales Manager in Column D. When you add up Column D, the sum will equal zero (0), if your calculations are correct. (Variances from zero may exist due to rounding).

Square each entry in Column C.

Example from Table 1:
Sales Manager
133.67 × 133.67 = 17868

Square each entry in Column D.

Example from Table 1:
Sales Manager
7.06 × 7.06 = 49.84

Multiply each entry in Column C by its corresponding entry in Column D.

Example from Table 1:
Sales Manager
133.67 × 7.06 = 943.71

After you've added up each column, use the data from this table to calculate the slope and constant.

The slope indicates how much the dependent variable - job rate - will change for one point change in the job value - the independent variable. The formula for the slope is (data from Table 1 is used):

Slope = sum of Column G ÷ sum of Column E
0.0380 = 3529.77 ÷ 92838

The constant is the hypothetical job rate at zero job value. After the slope is calculated, the constant is determined by using the following formula (data from Table 1 is used):

Constant = ( mean of Y ) - [ slope x (mean of X) ]
0.7695 = 25.90 - [0.0380 × 661.33]

Once you have determined the pay equity job rates, you need to calculate how well the job rate line fits the given set of data. R-squared is one measure used to assess this. A higher value of R-squared indicates a better fit.

The following table shows the results of the R-squared calculation based on the data contained in Table 1. Some of the data in Table # 2 will be used to clarify the final steps in this exercise.

Table 2
Example of the R-Squared Calculation (based on Table 1 data)
Male Job Classes	Job Value (X)	Job Rate $ (Y)	Predicted Job Rate $ (Pred. Y)	Error in Prediction $ (E)	Square of error (SQE)
	A	B	C	D	E
Sales Manager	795	32.96	30.98	1.98	3.92
Marketing Manager	770	29.88	30.03	-0.15	0.02
Controller	762	28.35	29.73	-1.38	1.90
Warehouse Manager	700	25.81	27.37	-1.56	2.43
Market Analyst	660	25.30	25.85	-0.55	0.30
Sales Representative	630	26.83	-24.71	2.12	4.49
Accountant	610	24.00	-23.95	0.05	0.00
Programmer	555	21.00	21.86	-0.86	0.74
Shipper/ Receiver	470	19.00	18.63	0.37	0.14
Sum					13.94

Step 2:
Prepare data for Table # 2 (R-squared)

Print the blank Table 2-a (looks exactly like Table # 2 above, but with empty cells) and start entering your own data using the step-by-step instructions and examples below.

Enter the male job classes in the Male Job Classes column.

Enter the male job values in Column A.

Enter the male job rates in Column B.

Calculate the predicted or pay equity job rate (Column C) for each male job class by using this formula:

Calculate Column D, which is the difference between the actual job rate in Column B ($32.96) and the pay equity job rate in Column C ($30.98).
For example, Sales Manager, $32.96 - 30.98 = $1.98.

Column E equals the square of each entry in Column D.
For example, Sales Manager, $1.98 × 1.98 = 3.92.

Calculate the R-squared using the following formula:

R-squared =	*1 - (sum of Column E ÷ sum of Column F)**
=	1 - (13.94 ÷ 148.14)
=	0.9059**

* from Table 1

** This ratio indicates that .91 or 91% can be considered a good fit.

Step 3:
Calculate pay equity job rates for the female job classes

The final step in this manual regression process is to calculate the PV job rates for the unmatched female job classes.

Print the blank Table 3-a (looks exactly like Table # 3 below, but with empty cells) and enter your own data using the pay equity job rate formula below. You will be using the value for the slope and constant to determine the pay equity job rate for the female job classes.

For example, the pay equity job rate for the Secretary job class (value of 400 points) is determined by using the following formula:

pay equity job rate = constant + ( slope × job value )
$15.97 = 0.7695 + ( 0.0380 × 400 )

Table 3
Example of Pay Equity Job Rates and Adjustments
Female Job Classes	Job Value	Pay Equity Job Rate	Current Job Rate	Pay Equity Adjustment
Secretary	400	$15.97	$14.72	$1.25
Customer Service Clerk	390	15.59	14.50	1.09
Marketing Coordinator	380	15.21	16.00	0.00
Accounting Clerk	350	14.07	13.25	0.82
Receptionist	340	13.69	13.04	0.65

Pay equity job rates are now calculated for all unmatched female job classes (as shown in Table # 3) for the fictitious organization used in this exercise.

Sample data and blank forms:

Now you know how to manually calculate proportional value job rates, you can try your own calculations. Three blank worksheets are provided for your use. You can print and complete these manually:

Table 1-a - Manual Regression Calculation
Table 2-a - R-squared Calculation
Table 3-a - Pay Equity Job Rates and Adjustments

Calculate a Regression Line- Manually -

Step 1:Prepare data for Table # 1 (Manual Regression Calculation)

Step 2:Prepare data for Table # 2 (R-squared)

Step 3:Calculate pay equity job rates for the female job classes

Sample data and blank forms:

Calculate a Regression Line
- Manually -

Step 1:
Prepare data for Table # 1 (Manual Regression Calculation)

Step 2:
Prepare data for Table # 2 (R-squared)

Step 3:
Calculate pay equity job rates for the female job classes