## The Basics of Regression Analysis

written by: N. Plowman • edited by: Michele McDonough • updated: 5/14/2013

A common statistical method used in Six Sigma is regression analysis, which allows predictions to be made based on the presence of a linear relationship between two variables. This article explores how this is significant in Six Sigma and further explains the regression analysis process.

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### Formulating Predictions

The goal of Six Sigma is to improve the quality and productivity of a project team or company. In order to accomplish this goal, Six Sigma proponents use a variety of statistical methods to determine whether observed results were in alignment with what was expected, one of which is a Chi-Square test. Another similar statistical test often used in Six Sigma is a regression analysis, which allows predictions to be made from observed and expected values.

A regression analysis enables one to determine whether a relationship exists between two variables. This is highly useful because it means that a regression analysis can be used to determine whether one variable, an independent variable, can be used to predict another variable, a dependent variable. The stronger the relationship is between two variables, such as process modification and defective rates, the greater the accuracy in predicting the defective rates for a particular process modification.

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### Regression Analysis in Plain Language

Simply stated, regression analysis is a statistical method that determines the extent to which a relationship exists between two variables. If the relationship is strong enough, one can then accurately predict the values of one variable based on the values of another using a simple linear formula.

There are many different types of relationships that can be identified, such as a curvilinear, u-shaped, or exponential relationship. However, the more common relationship, and the relationship that enables one to easily predict the value of a dependent variable, is the straight-line linear relationship.

To determine whether a relationship exists between two variables, one must plot the values on a graph, in which the independent variable is on the X-axis and the dependent variable is on the Y-axis. Since the dependent variable is what one is hoping to predict, the simple linear formula is Y = bo + b1X, in which:

• Y is the value of the dependent variable
• b0 is the Y-intercept, which is the value of Y when X=0
• b1 is the slope, which is the change in Y per one unit change in X
• X is the value of the independent variable

Using a regression analysis, one can accurately identify the best-fit line to minimize the variance between the sample data values and the imposed line. Once the best-fit line can be identified, the variables on the right-hand side of the simple linear formula can be calculated, enabling one to accurately predict the value of Y.