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Pay Equity Ontario > English (Canada) > Learn More > Our Guides and Tools > Calculate a Regression Line Manually

Create a wage line manually by following the steps outlined on this page.

#### There are the three main tasks:

1. Entering male job class information in a table and performing regression calculations on this data
2. Calculating the numbers needed for this regression line equation:
pay equity job rate = constant + ( slope × job value )
3. Applying the statistical calculation results to the female job classes to produce pay equity job rates

#### Sample data and blank forms:

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

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

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​​.

​A​C​E​G
​Job Value (X)Deviation from Average Job Value (X-XM)​Square  of (X-XM)Product of (X-XM)(Y-YM)
​Sales Manager​795​32.96133.67​​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
​Sum​5952​\$233.13​*0.03​*\$0.03​92838​148.14​3529.77
​Mean (Average)​661.33​\$25.90

## Step 1: Pr​​epare 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.

### a) Calculate Columns A and B

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

Example from Table 1: Add the data in Column A and calculate the mean, or average. Do the same for Column B.

 ​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​

### b)Calculate Column C

Example from Table 1: Substract the average job value from Column A from the job value of each job class​.

 ​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).​ ​

### ​c)Calculate Column D

Example from Table 1: Substract the average job rate from Column B from the job rate of each job class

 ​​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). ​

Example from Table 1: Square each entry in Column C​.

 ​Sales Manager ​133.67 × 133.67 = 17868

### e)Calculate Column F

Example from Table 1: Square each entry in Column D.

 ​Sales Manager ​7.06 × 7.06 = 49.84

### f)Calculate Column G

Example from Table 1: Multiply each entry in Column C by its corresponding entry in Column D.

 ​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.

### h)Calculate the Slope

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

### i)Calculate the Constant

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).

​A​C​E
Job Value(X) Predicted Job Rate \$ (Pred. Y) ​Square of error(SQE)
​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​-23.950.05​0.00​
​Programmer​555​21.00​21.86​-0.86​0.74
​Sum​13.94

## Step 2: P​​repare 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.

### a)First Column

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

### b)Column A

Enter the male job values in Column A.

c)Column B
Enter the male job rates in Column B.

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

 ​pay equity job rate = ​constant + ( slope × job value of male job class) ​\$30.98 = ​0.7695 + ( 0.0380 × 795 (Sales Manager)
e)Calculate Column D
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.

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

g)Add all the data in Column E
h)Calculate R-squared
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 pa​y 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.

 ​Job Value  ​Current Job Rate ​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.