# Developing the Predictive Equation

Once the Scatter plot has been used to find out the correlation between the inputs being measured as well as the desired outputs, it is now time to come up with an equation which shows the precise relationship. This is called Regression. Regression is a technique which summarizes the relationships observed in the Scatter plot in the form of an equation.

### How Regression is Used ?

In most Six Sigma projects, today the process of coming up with the regression equation is computerised. Hence the personnel need not understand the details that are involved within it. However they need to be well versed with the various types of regression equations. They are as follows:

### Types of Regression

• Linear Regression: In this type of regression there is only one input variable and one output variable in question. The input variable is the independent variable and the output variable is the dependant variable. Earlier we had stated the Six Sigma equation in the form of y = f(x).

A typical linear regression equation would look like:

Y = 1.5 + 2x

• Multi-linear Regression: In this type of regression there are multiple input variables and only one output variables. These equations are considerably more difficult to create. They are used to check the combined effect that multiple variables have on the output parameter.

• Non-Linear Regression: These are complex types of regression equations. They are rare. However in some cases they may be important to come up with. However the Six Sigma team should take the help of a trained expert who is well versed with the subject matter. Coming up with wrong regression calculations can be very harmful to a process.

### Application of the Predictive Equation

The Six Sigma team can now answer questions about the effect that the input variable has on the output. They can then decide as top whether the effect is significant when compared to the other variables. They can also decide the correct level of input (x) that needs to be maintained if an output (y) needs to be achieved.

For example:

Service Time = 3 minutes + 2.3 times × Handle time

Let’s say we want the service time to be 7 minutes as per the results we have got from the Voice of Customer. Therefore the handle time should be :

7 - 3 minutes = 2.3 × Handle time

4 minutes = 2.3 × Handle time

4/2.3 = Handle time

Therefore handle time must be 1.74 minutes if the process needs to meet the expectations of the customers.

This is how the regression equation can help us understand whether a factor is significant. It also helps us work the level of inputs required to get the desired output.

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Six Sigma - Analyze Phase